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Propositional logic is the study of propositions, where a proposition is a statement that is either true or false. Propositionallogic may be used to encode simple arguments that are expressed in natural language, and to determine their validity. The validity of an argument may be determined from truth tables, or using the inference rules such as modus ponens to establish the conclusion via deductive steps. Predicate logic allows complex facts about the world to be represented, and new facts may be determined via deductive reasoning. Predicate calculus includes predicates, variables and quantifiers, and a predicate is a characteristic or property that the subject of a statement can have. The universal quantifier is used to express a statement such as that all members of the domain of discourse have property P, and the existential quantifier states that there is at least one value of x has property P.

With the rapid development of artificial intelligence and the increasing demand for legal intelligence, using AI methods to predict legal judgments has become a hot spot in recent years. Charge prediction is one of the core tasks of Legal Judgment Prediction (LJP). It aims to predict charge from complicated legal facts, so as to help the court make judgments or provide legal professional guidance to non-professionals. In the field of legalAI, interpretability is crucial compared to others. Reasonable interpretability can eliminate hidden dangers such as gender discrimination and provide support for judges’ decisions. However, how to add the legal theory framework to the modeling to improve the interpretability is a challenge, which has few researches at present. To address this problem, we use Double-layer Criminal System as a guide to build Charge Prediction modeling called DCSCP which aims to predict charges in the criminal law of China. In general, our characteristic is to achieve multi-granularity inference of legal charges by obtaining the subjective and objective elements from the fact descriptions of legal cases. Specifically, our approach is performed in two steps: (1) extract the objective elements from the fact description and use them to generate candidate charges to achieve coarse-grained prediction; (2) extract the subjective elements from the fact description, and design the first-order predicate logic inference to realize the fine-grained charge inference in combination with the candidate charges. Experimental results show that our DCSCP can provide interpretable predictions, and it can maintain performance compared to other state-of-the-art charge prediction models.

In this paper, we discourse an analysis of classical first-order predicate logic as a constraint satisfaction problem, CSP. First, we will offer our general framework for CSPs, and then apply it to first-order logic. We claim it would function as a new semantics, constraint semantics, for logic. Then, we prove the soundness and completeness theorems with respect to the constraint semantics. The latter theorem, which will be proven by a proof-search method, implies the cut-elimination theorem. Furthermore, using the constraint semantics, we make a new proof of the Craig interpolation theorem. Also, we will provide feasible algorithms to generate interpolants for some decidable fragments of first-order logic: the propositional logic and the monadic fragments. The algorithms, reflecting a ‘projection’ of an indexed relation, will show how to transform given formulas syntactically to obtain interpolants.

Creating computing systems able to address our ever-increasing needs, especially as we reach the end of CMOS transistor scaling, will require truly novel methods of computing. However, the traditional logic abstractions and the digital design patterns we understand so well have coevolved with the hardware technology that has embodied them. As we look past CMOS, there is no reason to think that those same abstractions best serve to encapsulate the computational potential inherent to emerging devices. We posit that a new and radically more efficient foundation for computing lies at the intersection of superconductor electronics and delay-coded computation. Building on recent work in race logic, we show that superconducting circuits can naturally compute directly over temporal relationships between pulse arrivals; that the computational relationships between those pulse arrivals can be formalized through a functional extension to a temporal predicate logic used in the verification community; and that the resulting architectures can operate asynchronously and describe real and useful computations. We verify our hypothesis through a combination of detailed analog circuit models and layout designs, a formal analysis of our abstractions, and an evaluation of several superconducting temporal accelerators.

In this article, the subject of research is the sub-process of controlling the assignment of requisites to the electronic document of the process of registration and preparation of completed electronic documents for transfer to archival storage in the electronic document management system. The aim of the research is to develop a method for automatic control of the assignment of details to a completed electronic document. In the course of the study, the requirements of regulatory legal acts of federal executive bodies in the field of office work and archiving were analyzed, in terms of the registration of electronic files and their preparation for transfer to archival storage, scientific publications covering the issues of automation of office work in electronic office systems. A functional model was built for the process of control of registration and preparation for the delivery of electronic files for archival storage using the IDEF 0 methodology in a model for performing the sub-process of assigning details to a completed electronic document of the process of controlling registration and preparation for the delivery of electronic documents using the theory of logic (predicate logic). A method has been developed for automatic control of the assignment of requisites to a completed electronic case, which can be used in the design of advanced electronic document management systems, as well as modernization of existing ones by creating software modules that implement the functions of automatic control of the registration of completed electronic cases. This method makes it possible to increase the efficiency of the process of preparing completed electronic files for transfer to archival storage.

The article proposes the use of geospatial information to support managerial decision-making by public authorities in the field of reintegration of temporarily occupied territories in Donetsk, Luhansk regions and Crimea. Variants of application of decision support systems in the management of immovable military property of the Armed Forces of Ukraine, the existing algorithms and methods of the decision support system in land relations are analyzed. Proposals are presented to support the adoption of managerial decisions by public authorities on the basis of Earth remote sensing data. The algorithm for the functioning of the decision support system in solving the problems of reintegration of temporarily occupied territories has been improved. The proposed sequence of actions of the method of the process of supporting the adoption of administrative decisions by public authorities in the field of reintegration of temporarily occupied territories using geospatial information, mathematical constructions of category theory and predicate logic. The order of implementation of the sequence of actions of this method is given. By improving and detailing the proposed method, it is possible to form a more effective system for supporting the adoption of managerial decisions by public authorities using geospatial information. У статті запропоновано використання геопросторової інформації щодо підтримки прийняття управлінських рішень органами державної влади у сфері реінтеграції тимчасово окупованих територій у Донецькій, Луганській областях та в Криму. Проаналізовані варіанти застосування систем підтримки прийняття рішень в управлінні нерухомим військовим майном Збройних Сил України, існуючі алгоритми та методи системи підтримки прийняття рішень в земельних відносинах. Надані пропозиції щодо підтримки прийняття управлінських рішень органами державної влади на основі даних дистанційного зондування Землі. Удосконалений алгоритм функціонування системи підтримки прийняття рішень при вирішенні задач реінтеграції тимчасово окупованих територій. Запропонована послідовність дій методу процесу підтримки прийняття управлінських рішення органами державної влади у сфері реінтеграції тимчасово окупованих територій з використанням геопросторової інформації, математичні конструкції теорії категорій і логіки предикатів. Наведений порядок реалізації послідовності дій даного методу. Удосконалюючи та деталізуючи запропонований метод, можливо сформувати більш ефективну систему підтримки прийняття управлінських рішень органами державної влади з використанням геопросторової інформації.

The authors propose analogical reasoning systems based on first-order predicate logic using deep learning. The proposed systems consist of a model combining recursive neural networks and Word2Vec. When unknown data is input in this trained model, similar outputs to those of the trained data are obtained. Previous studies on symbolic inference using deep learning have focused on deductive and inductive inferences, and they require rule templates that are manually created and provided to the models in advance. However, it is not enough to infer unknown rules from a large amount of data on the Internet. Analogical reasoning is a mode of inference that attempts to solve a new case based on similarity. Thus, it enables inference of rules that were challenging to comprehend in previous studies. As a result of the experiments, unknown rules can be efficiently inferred from known rules contained in the knowledge bases. Using the proposed systems, the authors can extract unknown rules from five of the eight datasets consisting of three types of knowledge bases described in Prolog. The proposed method is the first case of analogical reasoning based on the first-order predicate logic using deep learning. Furthermore, the models used in the proposed systems have shown high robustness when using Word2Vec. For this reason, it is suggested that the practical applications of the proposed systems enable efficient inferences from a large amount of data that include noisy data on the Internet.

Information on rainfall prediction has great significance in agricultural fields where most of the crop’s irrigation depends on the rain water. Thus, rainfall prediction is a mandatory and an important process recently. Classical logic is further extended into fuzzy logic. Fuzzy logic has many advantages over classical logic. Two types of connotations of Fuzzy logic are: In narrow sense, Fuzzy Logic is a logical system, which is an extension of multivalued logic. The expert system of fuzzy consists of linguistics rules concerning the input variable of the fuzzy membership functions to the output variable of the fuzzy membership function. Fuzzy production rule IF-THEN statements relate the input variables of each other to define the result. Predicate logic operators such as AND operator is used to relate input and output variable. This paper proposed the prediction of rainfall using expert system model based fuzzy logic system for the demanding operational responsibilities needed by the meteorological department in the nation.

This study introduces a developed method to a smart computer-aided design/manufacturing (CAD/CAM) system, where layout design, process planning, and comprehensive computerized numerical control (CNC) code generation can be implemented to satisfy laser cutting holes, tapping, irregular and complicated profile processing, engraving, and burr back-scraping. The smart CAD/CAM(SCAM) system is developed as a commercial software product or application and firstly applied to flexible sheet metal machining center (BGL 130R). In this study, a formal modeling method involving Petri nets and first-order predicate logic is proposed to develop the smart manufacturing system. High-level Petri nets are employed to achieve the formal application architecture design of data flow for various functions, and the first-order logic used to represent the process plan is defined and deduced according to the machining methods. The developed system possesses the following characteristics: (1) a sound and complete deductive system to implement various types of trajectory planning, automatic generation, and validation of the CNC code; (2) a convenient design input environment and readiness for re-design and modification by adding specific design functions and using standard design procedures on a widely used CAD/CAM package; (3) helpful for designers in sheet metal layout designing, layout interference detection, process planning validation, preprocess manufacturing operation of CNC code generation, and autodefinition of storable file names; and (4) formal and simple in human–computer interaction, automatic and intelligent in process operations, and satisfactory in terms of the requirements of the flexible sheet metal machining center (BGL 130R).

In this paper, we present a novel constraint solving method for a class of predicate Constraint Satisfaction Problems (pCSP) where each constraint is represented by an arbitrary clause of first-order predicate logic over predicate variables. The class of pCSP properly subsumes the well-studied class of Constrained Horn Clauses (CHCs) where each constraint is restricted to a Horn clause. The class of CHCs has been widely applied to verification of linear-time safety properties of programs in different paradigms. In this paper, we show that pCSP further widens the applicability to verification of branching-time safety properties of programs that exhibit finitely-branching non-determinism. Solving pCSP (and CHCs) however is challenging because the search space of solutions is often very large (or unbounded), high-dimensional, and non-smooth. To address these challenges, our method naturally combines techniques studied separately in different literatures: counterexample guided inductive synthesis (CEGIS) and probabilistic inference in graphical models. We have implemented the presented method and obtained promising results on existing benchmarks as well as new ones that are beyond the scope of existing CHC solvers.

The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed. The photo shows a prototype sculpture for the cube.

Petri net (PN) is an effective modeling and analysis tool for discrete event systems. By attaching a first-order logic predicate logic formula to a transition in a PN, a high-level Petri net named Logic Petri Net (LPN) is obtained. LPN has been proved to have equivalent modeling capability with inhibition Petri nets but keeps simpler net structures than the latter. It has the advantage of modeling the cooperative systems with the function to process batch and indeterminate resources. This paper proposes a vector computational method for LPN compositional analysis. It studies the composition of LPNs with the shared P-type subnets. Each logical expression is transformed into a unique disjunctive normal one and then into a unique set of vectors. A vector computational method is proposed such that the properties of the composition of the shared P-type subnets such as liveness, boundedness, and reversibility are verified. An E-commerce system with customers, merchants, and a third-party is constructed to illustrate the method. This paper can improve the state of the art in the theory of LPNs.

We study the recognition problem in the metaprogramming of finite normal predicate logic programs. That is, let $\mathcal{L}$ be a computable first-order predicate language with infinitely many constant symbols and infinitely many $n$-ary predicate symbols and $n$-ary functions symbols for all $n \geq 1$. Then we can effectively list all the finite normal predicate logic programs $Q_0,Q_1,\ldots $ over $\mathcal{L}$. Given some property $\mathcal{P}$ of finite normal predicate logic programs over $\mathcal{L}$, we define the index set $I_{\mathcal{P}}$ to be the set of indices $e$ such that $Q_e$ has property $\mathcal{P}$. We classify the complexity of the index set $I_{\mathcal{P}}$ within the arithmetic hierarchy for various natural properties of finite predicate logic programs. For example, we determine the complexity of the index sets relative to all finite predicate logic programs and relative to certain special classes of finite predicate logic programs of properties such as (i) having no stable models, (ii) having no recursive stable models, (iii) having at least one stable model, (iv) having at least one recursive stable model, (v) having exactly $c$ stable models for any given positive integer $c$, (vi) having exactly $c$ recursive stable models for any given positive integer $c$, (vii) having only finitely many stable models, (viii) having only finitely many recursive stable models, (ix) having infinitely many stable models and (x) having infinitely many recursive stable models.

Interacting with mobile robots through natural language is the main concern of this article, which focuses on the semantic meaning of concepts used in natural language instructions to navigate robots indoors. Assuming the building structure is the prior knowledge of the robot and the robot has the ability of navigating itself locally to avoid collision with the environment, the building structure is represented with predicate logic on SWI-Prolog as the database of the indoor environment, which is called semantic map in this paper, in which the basic predicate clauses are based on two kinds of entities, namely ‘area' and ‘node.' The area names (in natural language convention) of indoor environment are organized with an ontology and are defined in the semantic map which includes the geometric information of areas and connection relationships between areas. With the semantic map database, functions for robot navigation, like a topological map, path planning, and self-localization, are realized through reasoning by properly designed predicates based on constraint satisfaction problem (CSP). An example building is given to show the idea proposed in this article, the real data of which was used to establish the semantic map, and the predicates for navigation functions worked well on SWI-Prolog.

International audience; One of the most common scenarios of handling incomplete information occurs in relational databases. They describe in-complete knowledge with three truth values, using Kleene’s logic for propositional formulae and a rather peculiar exten-sion to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and pred-icate logics?Our goal is to answer this question. Using an epistemic ap-proach, we first characterize possible levels of partial knowl-edge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connec-tives of the propositional logic, and prove that Kleene’s logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For exten-sions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete informa-tion represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpreta-tion of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.

Since years, the logic course in the first year of our Bachelor program in Computer Science, dealing with propositional and predicate logic, suffers from poor pass rates. The students perceive the formal and abstract mechanisms of logic as difficult and awkward to deal with. Many students do not study the course material on a regular basis, which results in poor mastery of the basic concepts and principles. Consequently, students often fall behind as the course progresses. Previous attempts to remedy this procrastination behavior had little success. Since educational games are commended as an enjoyable way to foster learning, we decided in 2016 to develop an educational game for the course. This game, called TrueBiters, is a two-player competitive game inspired by an existing card game. We adapted this card game to propositional logic and digitized it as an app. The development was done in an iterative way. Each version was evaluated and using the received user feedback and evaluation results the game was improved and reevaluated. Based on the results of the evaluations we can conclude that the game is well suited for its target audience, i.e., logically-mathematically intelligent people, and is a good supplement, and even replacement for some of the traditional face-to-face exercise sessions. However, we also learned that a proper embedding into the course is needed to ensure that all students actually use the game and benefit from playing it. In this paper we present the game, explain and motivate its evolution, discuss the evaluations performed, and present lessons learned.

Association rule mining (ARM) is used for discovering frequent itemsets for interesting relationships of associative and correlative behaviors within the data. This gives new insights of great value, both commercial and academic. The traditional ARM techniques discover interesting association rules based on a predefined minimum support threshold. However, there is no known standard of an exact definition of minimum support and providing an inappropriate minimum support value may result in missing important rules. In addition, most of the rules discovered by these traditional ARM techniques refer to already known knowledge. To address these limitations of the minimum support threshold in ARM techniques, this study proposes an algorithm to mine interesting association rules without minimum support using predicate logic and a property of a proposed interestingness measure (g measure). The algorithm scans the database and uses g measure’s property to search for interesting combinations. The selected combinations are mapped to pseudo-implications and inference rules of logic are used on the pseudo-implications to produce and validate the predicate rules. Experimental results of the proposed technique show better performance against state-of-the-art classification techniques, and reliable predicate rules are discovered based on the reliability differences of the presence and absence of the rule’s consequence.

Reference and encyclopedic book editions are characterized by complex technical and semantic features. Such editions contain articles that answer the predicted questions of potential consumers in a concise form and have semantic and compositional integrity, and text elements are characterized by a clearly defined structure, which is provided by the use of headings, sections, subheadings, etc. It is difficult to imagine the process of cognition of a particular subject area without the use of reference and encyclopedic editions. The challenges facing the humanity require immediate reactions, which is why the lion’s share of reference and encyclopedic editions are now presented in electronic form. This transformation has not solved the design problem, but on the contrary, deepened it, increasing the variability of the necessary parameters selection. Reference and encyclopedic editions have many structural differences from other types of editions (art, popular science, etc.), the identification with which is unacceptable in terms of quality assurance. In view of the above, based on expert decisions, a set of factors of influence on the design process of reference and encyclopedic book editions has been singled out, a semantic network has been constructed and described, priority levels of factors have been established, a model of priority influence of factors on the quality of the analysed technological process has been constructed and optimized. The means of graph and network theory, elements of predicate logic, iterative methods, means of the hierarchical systems theory, methods of multicriteria optimization and pairwise comparisons have been used.

The paper is devoted to the application of model-theoretical methods for extraction of knowledge from medical texts and documents and its formal representation. The aim of the work is to automate the filling of knowledge bases of the IACPaaS platform using knowledge from texts of disease descriptions. IACPaaS is a cloud platform for the development, management and remote use of intelligent cloud services. The peculiarities of disease description texts are the presence of medical word terms (such as “blood pressure”) and the abundance of sentences with clauses and homogeneous sentence members. To solve the problem of knowledge extraction, methods of transforming natural language sentences into quantifier-free formulas of the first-order predicate logic are used. Knowledge extracted from texts is formalized in the form of sets of atomic sentences that form fragments of atomic diagrams of algebraic systems. Further, a knowledge tree is built from the fragments of atomic diagrams, which serves as an intermediate representation of knowledge for subsequent translation into the format of IACPaaS information resources. The software system allows medical workers to fill knowledge bases with descriptions of diseases in shorter time, and gives the opportunity to check the consistency of the obtained formal specifications automatically.

International audience; Constructive foundations have for decades been built upon realizability models for higher-order logic and type theory. However, traditional realizability models have a rather limited notion of computation, which only supports non-termination and avoids many other commonly used effects. Work to address these limitations has typically overlaid structure on top of existing models, such as by using powersets to represent non-determinism, but kept the realizers themselves deterministic. This paper alternatively addresses these limitations by making the structure underlying realizability models more flexible. To this end, we introduce evidenced frames: a general-purpose framework for building realizability models that support diverse effectful computations. We demonstrate that this flexibility permits models wherein the realizers themselves can be effectful, such as λ-terms that can manipulate state, reduce non-deterministically, or fail entirely. Beyond the broader notions of computation, we demonstrate that evidenced frames form a unifying framework for (realizability) models of higher-order dependent predicate logic. In particular, we prove that evidenced frames are complete with respect to these models, and that the existing completeness construction for implicative algebras-another foundational framework for realizability-factors through our simpler construction. As such, we conclude that evidenced frames offer an ideal domain for unifying and broadening realizability models.

Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of characterizing (classes of) structures are of fundamental interest and can be highly non-trivial to answer. We investigate several problems regarding the homomorphism closure (homclosure) of the class of all (finite or arbitrary) models of logical sentences: membership of structures in a sentence's homclosure; sentence homclosedness; homclosure characterizability in a logic; normal forms for homclosed sentences in certain logics. For a wide variety of fragments of first- and second-order predicate logic, we clarify these problems' computational properties.

This paper extends the results of Hermida's thesis about logical predicates to more general logical relations and a wider collection of types. The extension of type constructors from types to logical relations is derived from an interpretation of those constructors on a model of predicate logic. This is then further extended to n-ary relations by pullback. Hermida's theory shows how right adjoints in the category of fibrations are composed from a combination of Cartesian lifting and a local adjunction. This result is generalised to make it more applicable to left adjoints, and then shown to be stable under pullback, deriving an account of n-ary relations from standard predicate logic. A brief discussion of lifting monads to predicates includes the existence of an initial such lifting, generalising existing results.

The subject of the study in the article is flexible integrated robotic systems. The aim of the work is to integrate models and decision-making methods in order to create information technology for flexible production. The following tasks are solved in the article: analysis of current trends in the development of production systems, consideration of intellectual decision-making systems as one of the key elements of automated control systems, consideration of the creation of information technology, based on a set of methods and decision models, including adaptive decision making for non-deterministic tasks. Research methods are the theory of sets and the theory of predicates. The following results were obtained: the main problems of the development of flexible integrated systems of modern production were analyzed and formulated. As a new element in the technological systems, it is proposed to introduce the intelligent production agents implemented as mobile robotic platforms capable of performing transport and assembling functions, executing the monitoring tasks, and establishing the basic requirements for them. From the formal point of view, the decision-making process in flexible robotic systems is considered, based on the interaction of the properties of the robotic system, the properties of the working space and the set of possible solutions. The fulfillment of each individual technological task involves the development and implementation of a plan of work of robotic equipment, the set of variants of which is a strategy of functioning of the intellectual robotic system, described in the form of predicate logic. To solve the required technological tasks, the use of the automatic procedures of the generator of solutions, which operates based on the frame-like structures is proposed. The decision-making process consistently supports the consistent decision-making information technology in a robotized production system based on the models of different types. Conclusions: application of the concept of the intellectual agent in the production environment requires the integrated application of models and methods of decision making, which can be a separate information technology of robotic production.

Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic programming, are widespread declarative programming techniques. In logic programming, there is a gap between the meta-programming practice and its theory: The formalisations of meta-programming do not explicitly address its impredicativity and are not fully adequate. This article aims at overcoming this unsatisfactory situation by discussing the relevance of impredicativity to meta-programming, by revisiting former formalisations of meta-programming and by defining Reflective Predicate Logic, a conservative extension of first-order logic, which provides a simple formalisation of meta-programming., Comment: Under consideration for publication in Theory and Practice of Logic Programming

In this paper, a new process learning framework that is based on probabilistic learning and predicate logic is proposed. The input of this framework is a set of log files, and the output is a probabilistic predicate-based workflow that describes the process. This paper targets a methodology of learning processes given data and the learning algorithm finds out the logical operators that bind the events described in data and model it using predicate logic. While building the process, the probability of every event and the probabilities of the relationship between events are calculated. The learning process is an ongoing process, which means after learning when feeding the system with a new set of log files, the algorithm takes the previously learned process and it is set of probabilities as a starting state and starts modifying them based on the newly learned log files. This feature is very essential for those applications that integrate and interact with bigdata since for bigdata, starting the learning process from the beginning for every new set of data is not feasible. In this paper, the assumption is that log files are event-based, and every event is associated with its time of occurrence. Any event could have multiple occurrence times throughout the log files. The framework provides an optimal general definition of a process that is described by those log files. The process could change schematically or with respect to behavior when learning a new set of logs. In order to achieve what is described, a dependency matrix needs to be learned, and then the probability matrix is calculated. The outcome of the two matrices is a predicate-based workflow. Workflows can easily be described by Petri nets and Petri nets can map to predicate logic. The reason to convert the workflow into the knowledge base is the ability to infer new facts from given facts we conclude from log files. In this paper, we integrate a modification to α algorithm with the framework in order to describe dependencies and probability of occurrences of events.

This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.

Formal logic expressions are commonly written in standardized mathematical notation. Learning this notation typically requires many years of experience and is not an explicit part of undergraduate academic curricula. Constructing and comprehending logical predicates can feel difficult and unintuitive. We hypothesized that this process can be automated using neural machine translation. Most machine translation techniques involve word-based segmentation as a preprocessing step. Given the nature of our custom dataset, hosts first-order-logic (FOL) semantics primarily in unigram tokens, the word-based approach does not seem applicable. The proposed solution was to automate the translation of short English sentences into FOL expressions using character-level prediction in a recurrent neural network model. We trained four encoder-decoder models (LSTM, Bidirectional GRU with Attention, and two variants of Bi-directional LSTM with Attention). Our experimental results showed that several established neural translation techniques can be implemented to produce highly accurate machine translators of English sentences to FOL formalisms, given only characters as markers of semantics. We also demonstrated that attention-based enhancement to the encoder-decoder architecture can vastly improve translation accuracy. Most machine translation techniques involve word-based segmentation as a preprocessing step. Given the nature of our custom dataset, hosts first-order-logic (FOL) semantics primarily in unigram tokens, the word-based approach does not seem applicable. The proposed solution was to automate the translation of short English sentences into FOL expressions using character-level prediction in a recurrent neural network model. We trained four encoder-decoder models (LSTM, Bidirectional GRU with Attention, and two variants of Bi-directional LSTM with Attention). Our experimental results showed that several established neural translation techniques can be implemented to produce highly accurate machine translators of English sentences to FOL formalisms, given only characters as markers of semantics. We also demonstrated that attention-based enhancement to the encoder-decoder architecture can vastly improve translation accuracy. We trained four encoder-decoder models (LSTM, Bidirectional GRU with Attention, and two variants of Bi-directional LSTM with Attention). Our experimental results showed that several established neural translation techniques can be implemented to produce highly accurate machine translators of English sentences to FOL formalisms, given only characters as markers of semantics. We also demonstrated that attention-based enhancement to the encoder-decoder architecture can vastly improve translation accuracy.

Consider the following puzzle: given a number, remove k digits such that the resulting number is as large as possible. Various techniques are employed to derive a linear-time solution to the puzzle: we justify the structure of a greedy algorithm by predicate logic, give a constructive proof of the greedy condition using a dependently typed proof assistant and calculate the greedy step as well as the final, linear-time optimisation by equational reasoning.

We formalize a fragment of the theory of institutions sufficient to establish basic facts about the institution "Image missing" for Event-B, and its relationship with the institution "Image missing" for first-order predicate logic. We prove the satisfaction condition for "Image missing" and encode the institution comorphism "Image missing" embedding "Image missing" in "Image missing" .

Models evolved from mere pictures supporting human understanding to sophisticated knowledge structures processable by machines. This entails an inevitable need for computer-understandable models and languages and causes formalization to be a crucial part in the lifecycle of a modeling method. An appropriate formalism must be a means for providing a unique, unambiguous but implementation-independent way of specifying arbitrary modeling languages and for this purpose must be generic and open to capture any domain and any functionality. In this paper we give a pervasive description of the formalism MetaMorph based on predicate logic – an approach fulfilling these requirements. This is done with an extensive proof-of-concept case illustrating the application of the formalism concept by concept. For the case study we use the modeling language ProVis from the domain of stochastic education. The language ProVis comprises only few objects and relation types but with high interconnection and therefore appears as a interesting specimen for formalization and showing the feasibility of the demonstrated approach.

The study of quantification has become a significant area of research among logicians, philosophers, linguists, computer scientists, and others. Related to quantification, the form of generalized quantifiers is generally found in natural language. However, another type of quantifiers, which is called fuzzy and vague and they always need sort of proper treatment and resolution. Many proposals like (‘the fuzzy inclusion relation’ and ‘monotonicity in the ith argument’) have been introduced to deal such issue. Here, we especially focus on to a natural language (Punjabi) to study few but important fuzzy quantifier cases that do not find in Hindi. We select 29 predicates and compare them in two data sets with these (ਭਰਾ-ਕ [porɑ-kʊ]; ਮਾੜਾ-ਜਾ [mɑɽɑ-ɟɑ]; ਜਮਹਾ-ਈ [ɟəmɑ-i]; and ਮਸਾ-ਕ [məsɑ-kʊ]) fuzzy quantifiers and suggest the mapping plan. After comparing both languages (Punjabi and Hindi), we claim that Punjabi has comparatively strong quantification and it can be discussed and analyzed in a predicate logic.

First-order logic is a generalization of propositional logic, which is also referred to as predicate logic. Predicate logic is a more powerful extension of propositional logic, which can perform more complex reasoning tasks in artificial intelligence that are not possible with the use of only propositional logic.

This chapter proposes a methodology to implement the uncertain linguistic summarizer posed in Liu’s uncertain logic to measure the performance of investment funds in the Colombian capital market. The algorithm extracts a truth value for a set of linguistic summaries, written as propositions in predicate logic, where the terms for the quantifier, subject, and predicate are unsharp. The linguistic summarizer proves to be autonomous, successful, efficient, and close to human language. Furthermore, the implementation has a general scope and could become a data mining tool under uncertainty. The propositions found characterize with plenty of sense the investment funds data. Finally, a Corollary that allows accelerating the obtention of the summaries is presented.

Software product line engineering improves software quality and diminishes development cost and time by efficiently developing software products. Its success lies in identifying the commonalities and variabilities of a set of software products which are generally modeled using feature models. The success of software product lines heavily relies upon the quality of feature models to derive high quality products. However, there are various defects that reduce profits of software product line. One of such defect is redundancy. While the majority of research work focuses on the identification of redundancies, their causes and corrections have been poorly explored. Causes and corrections must be as accurate and comprehensible as possible in order to support the developer in resolving the cause of a redundancy. This research work classified redundancies in the form of a typology. An ontological first-order logic rule based method is proposed to deal with redundancies. A two-step process is presented for mapping model to ontology based on predicate logic. First-order logic based rules are developed and applied to the generated ontology for identifying redundancies, their causes and corrections to resolve redundancies. The proposed method is illustrated using a case study from software product lines online tools repository. The results of experiments performed on 35 models with varied sizes of real world models as well as automatically generated models from the Software Product Line Online Tools repository and models created via FeatureIDE tool conclude that the method is accurate, efficient and scalable with FM up to 30,000 features. Thus, enables deriving redundancy free end products from the product line and ultimately, improves its quality. University Grants Commission (UGC), New Delhi, Government of India F117.1/201415/RGNF201415SCJAM66324

The B landscape can be confusing to formal methods outsiders, especially due to the fact that it is partitioned into classical B for software and Event-B for systems modelling. In this article we shed light on commonalities and differences between these formalisms, based on our experience in building tools that support both of them. In particular, we examine not so well-known pitfalls. For example, despite sharing a common mathematical foundation in predicate logic, set theory and arithmetic, there are formulas that are true in Event-B and false in classical B, and vice-versa.

Dependent refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type systems and predicate logic, that is, a construction of liftings of closed comprehension categories from given (underlying) closed comprehension categories and posetal fibrations for predicate logic. We give sufficient conditions to lift structures such as dependent products, dependent sums, computational effects, and recursion from the underlying type systems to dependent refinement type systems. We demonstrate the usage of our construction by giving semantics to a dependent refinement type system and proving soundness.

This paper addresses the issue of detecting and localizing failures in the distributed SCADA system based on the analysis of changes in the information flow states when passing through structural modules and levels of SCADA hierarchy. The structural and logical model presented describes SCADA of any topology. We formed diagnostic features to detect independent failures based on the characteristic functions of three-valued logic. We put forward a methodology of expert diagnostic systems to analyze changes in the state of SCADA information flows. We also developed a predicate system for knowledge representation in the expert system to implement a method for diagnosing SCADA operability when having incomplete or unreliable data. This includes a predicate system for describing SCADA topology and detecting the location of any failures. The configuration diagram of SCADA topology is presented using the parameters of the structural and logical model for diagnosing failures. This model is used by the predicate system within the expert system knowledge base. We calculate the instability coefficients to evaluate the operability of each system’s structural module in real-time based on the analysis of changes in the state of SCADA information flows within the structural and logical model developed. The proposed method for detecting and localizing failures in the SCADA system can be applied both for current diagnostics and for predicting the operability of the structural modules of the SCADA system. The system operability prediction will be formed on the basis of statistical processing and analysis of the retrospective array containing the instability coefficients of the SCADA structural modules’ operation.

A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that enables reasoning with defeasible rules is presented. Finally, reasoning by cases using an argumentation tableau is discussed.

This paper proposes a modeling method of college students’ online information query motivation based on statistical feature information fusion. The statistical sequence model of university students’ online information query motivation distribution big data is constructed, and the big data prediction of university students’ online information query motivation is carried out by using the method of restructuring the regional structure of big data space. The association rule distribution feature set of university students’ online information query motivation distribution big data is established, and the fuzzy correlation constraint control method is combined to predict university students’ online information query motivation. The decision tree model is used for big data test and template matching of college students’ online information query motivation in complex network environment, and the statistical sequence model of college students’ online information query motivation distribution big data is constructed. Predicate logic reasoning is used to realize the optimization prediction of the development direction of college students’ online information query motivation, and the subsection test method is used to control the optimization of data clustering center to realize the analysis model of college students’ online information query motivation. The simulation results show that this method has higher accuracy and better reliability in analyzing the motivation of college students’ online information query.

Like what we have done in the previous chapter, we will apply the same idea but this time to predicate logic otherwise known as First-Order Logic (FOL). Predicate logic is called FOL because the logic speaks about objects and their relationships with other objects. When we speak about something, we are predicating it, like in saying “John got infected by a virus”. In general, FOL speaks about individuals. When we are predicating on a predicate itself, or we are speaking about sets of sets, then this is now the realm of higher order logic (HOL), which is beyond our scope.

In this chapter we will supply you with some practical lessons in logic which you will normally employ in proving theorems. Although experts will consider our discussion light, yet you will be equipped with tools in the process of proving. We take our metaphor from the mechanic who usually could go away and fix most car issues by the simple use of pliers and screw drivers. You can get away using them but it won’t be absolutely efficient. We need more tools. For our case we need to be conversant with two useful classical logics: 1. Propositional Logic 2. First-Order Logic/Predicate Logic.

This chapter introduces relational probabilistic graphical models (RPGMs), which combine the expressive power of predicate logic with the uncertain reasoning capabilities of probabilistic graphical models. First, a brief review of propositional and predicate logic is presented. Then, two different relational probabilistic formalisms are described: probabilistic relational models and Markov logic networks. Finally, the application of the two previous approaches is illustrated in two domains, student modeling for a virtual laboratory and visual object recognition based on symbol-relational grammars.

Problem setting. The paper is the Part II of the large research, dedicated to both revision of the system of basic logical categories and generalization of the modern predicate logic to functional logic. Basic categories of functional logic are the following: an individual, a function, representation, and a sequence. Paper objective. T he main task of the paper is to describe every one of the categories in question. The more expansive task of all the paper series is to expose the whole system of functional logic and to prove its advantagies. Recent research and publications analysis. Functional logic was discovered by the author in 1997, and there is no investigation in this field up today except of papers of the autor. Paper main body. An individual is any theoretical object regarded as atomic. Functions are regarded as ambiguous in general case, maybe nullary, and are treated as methods to represent some (any) objects. Most important types of functions are individuals’ functions (for example, arithmetic operations), functionals, and operators. Representation is the ultimate generalization of equality; we treat representation as any specification of an object, as a way to make it present. Fundamentals of the theory of representation are following: any individual can be represented either by itself as a function, or by a nullary function, or via other objects by a function with argument places. The corrected form (with respect to the Paper I) of representation formulas, i. e., atomic formulas of functional logic are involved. The form of terms that represents general names in formal languages of functional logic is present. Both these corrections use the machinery of choice functions, i. e., functions that “elect” one value of any ambiguous function in any case of its use. A sequence treated as a basic nondefinable logical notion. The nondefinability of the notion of a sequence will be proved in another paper. When we operate with individuals, functions, and representation, we structure them in sequences such that every latter has the first element and is discrete (and many of them also have the last element). Conclusions of the research. An individual and a function are relative categories because, first, when we start to talk about a function, it became an individual with the name “such and such a function” and, secondly, when an individual is represented by itself, it became a function. Also, categories of an individual, a function, representation, and a sequence are basic but not universal for logic, i. e., not every logical object is either an individual or a function or representation or a sequence. Say, semantical categories of an expression, a sense, and a denotation are independent of four described above. This means that we described above the field of logic, independent from semantics. The author calls this field (and its theory) logistics.

Analysis of the existing occupational health and safety management systems at machine-building enterprises. Selection of personnel assessment by highlighting the main properties of the personnel that influence the reliability of their work. Development of indicators that describe each of them using a special technique, based on the selected properties. The possibility of using predicate logic for forming and using the properties and qualities of the personnel in the future when senior executives make a decision to maintain an appropriate level of the personnel reliability at the machine-building enterprises.