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This paper presents an agile method of logical semantics based on high-order Predicate Logic. An operator of predicate abstraction is introduced that provides a simple mechanism for logical aggregation of predicates and for logical typing. Monadic high-order logic is the natural environment in which predicate abstraction expresses the semantics of typical linguistic structures. Many examples of logical representations of natural language sentences are provided. Future extensions and possible applications in the interaction with chatbots are briefly discussed as well. [ABSTRACT FROM AUTHOR]

There are two general methods for interpreting and analyzing khārijī and ḥaqīqī propositions: first, by analyzing them within a unified logic; second, by assigning separate logics to khārijī and ḥaqīqī propositions. So far, most interpretations and analyses of khārijī and ḥaqīqī propositions have been carried out using the first method within either traditional logic or a branch of modern logic, while the second method has rarely been used for this purpose. In this article, we aim to use the second method and demonstrate that the appropriate logic for ḥaqīqī propositions is classical predicate logic, while for khārijī propositions, it is predicate-free logic. We show that non-classical predicate-free logic restricts the rules of introduction and elimination of the quantifiers on the existence of khārijī objects, making it the most suitable logic for khārijī propositions. In contrast, classical predicate logic, which does not restrict the quantifiers on the external existence of objects, is more suitable for ḥaqīqī propositions. Additionally, we illustrate that by incorporating modal logic and temporal logic into classical and free predicate logics, the principles and rules of ḥaqīqī and khārijī propositions become more distinguishable, resulting in more distinct logics. In particular, we demonstrate that the Barcan Formula, the Buridan Formula, and the converse Barcan Formula hold true for ḥaqīqī propositions and are proven in classical modal and temporal logics, while they are false for khārijī propositions and remain unprovable in free modal and temporal logic.

This paper presents an agile method of logical semantics based on high-order Predicate Logic. An operator of predicate abstraction is introduced that provides a simple mechanism for logical aggregation of predicates and for logical typing. Monadic high-order logic is the natural environment in which predicate abstraction expresses the semantics of typical linguistic structures. Many examples of logical representations of natural language sentences are provided. Future extensions and possible applications in the interaction with chatbots are briefly discussed as well.

В статье рассматривается логический подход к анализу данных для решения задачи классификации. Исследуемые данные представляют собой совокупность объектов и их признаков. Как правило, это разрозненная разнородная информация, и ее недостаточно для разумного применения вероятностных моделей. Поэтому рассматриваются логические алгоритмы, которые при определенных условиях могут оказаться более адекватными. Для выразительного формального представления отношений между объектами и их атрибутами используется многозначная логика, а количество значений зависит от конкретного атрибута. Поэтому предлагается система операций над переменными с разными областями определения. В результате строится решающая функция, которая является классификатором объектов, присутствующих в изучаемых данных. Анализируются свойства и возможности этой функции. Показано, что логическая функция, являющаяся конъюнкцией в пространстве правил, связывающих заданные объекты с их характерными признаками, однозначно характеризует исходные данные, делит предметную область на классы, обладает свойствами модифицируемости, удовлетворяет требованиям полноты и непротиворечивости в заданная область. В работе также предлагается алгоритм его реализации

This paper proposes a framework for time-efficiently finding multiple answers that meet multiple logical constraints and are Pareto-optimal for multiple objective functions. The proposed framework determines a set of optimal answers by iteratively replacing a set of definite clauses. Clause replacement is performed using a SAT solver consisting of equivalent transformation rules (ETRs). An ETR replaces a definite clause with one or more clauses while preserving the declarative meaning of the union of the original clause and problem clauses. To efficiently find optimal answers, in this paper, we define a new class of ETRs that are generated based on the evaluation results of a multi-objective genetic algorithm (MOGA) and propose a method for generating ETRs that belong to the new class. ETRs belonging to the new class help to replace definite clauses according to user objectives such as cost–benefit performance, reliability, and financial constraints. Thus, a SAT solver that uses the new ETR class in addition to extant ETR classes can preferentially replace definite clauses that produce the optimal answer for user objectives. Experimental results indicate that the proposed framework can significantly reduce the computation time and memory usage necessary to determine a set of optimal answers for user objectives. [ABSTRACT FROM AUTHOR]

As an indispensable technology of intelligent education, intelligent tutorial algorithms for solving mathematical or physical problems have attracted much attention in recent years. Nevertheless, since solving mechanics problems requires complex force analysis and motion analysis, current researches are mainly focus on solving geometry proof problems and direct circuit problems. There are some inherent challenges on developing such algorithms, including the low intelligence, mobility and interpretability of the comprehension algorithm. Therefore, this article develops a novel algorithm for solving mechanics problems. First, we propose a comprehension model for mechanics problems and convert problem understanding into relation extraction. Furthermore, a novel neural model combining pretrained model BERT and graph attention network (GAT) is proposed to extract the direct conditions of input mechanics problems. Second, a hidden information mining method is proposed for supplementing the conditions of the input problem. Third, a predicate logic based algorithm is proposed for force analysis. Finally, a solving algorithm is presented for choosing equations to acquire the solutions. Solving experiments and sensitivity analysis are provided to demonstrate the effectiveness of the proposed algorithm.

A notion of strictly primitive recursive realizability is introduced by Damnjanovic in 1994. It is a kind of constructive semantics of the arithmetical sentences using primitive recursive functions. It is of interest to study the corresponding predicate logic. It was argued by Park in 2003 that the predicate logic of strictly primitive recursive realizability is not arithmetical. Park's argument is essentially based on a claim of Damnjanovic that intuitionistic logic is sound with respect to strictly primitive recursive realizability, but that claim was disproved by the author of this article in 2006. The aim of this paper is to present a correct proof of the result of Park. [ABSTRACT FROM AUTHOR]

Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model value beyond mere comprehensible pictures. To enable this amplification and turn models into computer-processable structures, a comprehensive formalization is needed. This paper presents the formalism MetaMorph based on typed first-order logic and provides a perspective on the potential and benefits of formalization that arise for a variety of research issues in conceptual modeling. MetaMorph defines modeling languages as formal languages with a signature Σ —comprising object types, relation types, and attributes through types and function symbols—and a set of constraints. Four case studies are included to show the effectiveness of this approach. Applying the MetaMorph formalism to the next level in the hierarchy of models, we create M2FOL, a formal modeling language for metamodels. We show that M2FOL is self-describing and therefore complete the formalization of the full four-layer metamodeling stack. On the basis of our generic formalism applicable to arbitrary modeling languages, we examine four current research topics—modeling with power types, language interleaving & consistency, operations on models, and automatic translation of formalizations to platform-specific code—and how to approach them with the MetaMorph formalism. This shows that the rich knowledge stack on formal languages in logic offers new tools for old problems. [ABSTRACT FROM AUTHOR]

Due to the lack of language analysis and understanding algorithms for kinematics problems, researches on automatic algorithms for tutorial systems are mainly concentrated on mathematics and physical circuits, and these algorithms are still represented by frame solution and semantic analysis. Additionally, these methods need to design rule templates to understand the complex text, which leads to the low efficiency of solving. Although deep learning (DL) have be applied to machine answers, but it is difficult to achieve the integration of problem understanding, reasoning, and solving through a generic framework. Therefore, this paper proposes a high-performance algorithm to understand and solve kinematics problems. By dividing solving kinematics problems into two stages: understanding and solving, we propose a unified framework for solving kinematic problems. Firstly, we transform understanding into relation extraction (RE), and propose a RE algorithm combining named entity recognition (NER) and first order logic (FOL) based on a novel tagging schema to extract overlapping relation in kinematics texts. For the solving stage, a backward chain reasoning algorithm based on meta-information is presented to solve kinematics problems. Additionally, three levels of comprehension and two conditions for measuring levels of comprehension are proposed to evaluate the performance of the proposed system. Finally, based on the evaluation metrics proposed in this paper, verification experiments are carried out on a dataset of kinematic problems from an authoritative source. And the results show that the proposed algorithm successfully solves 92.52% of the kinematic problems, which is higher than the baseline algorithms. [ABSTRACT FROM AUTHOR]

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

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. [ABSTRACT FROM AUTHOR]

The similarity between logic and semantics of the Stoics and Frege has long been known, and it can be explained in various ways. In 2021, Susane Bobzien published a work in which she explains this similarity rather surprisingly: she hypothesizes that Frege generously helped himself with the foundations of Stoic logic as it was published in the first volume of History of Logic in the West by Carl Prantl. However, this hypothesis encounters various problems. The key point of the whole accusation is founded on the formulation of a general proposition in language using implication and anaphora, which Frege supposedly took from the Stoics, although in Prantl's text there is only one example of a sentence with this structure. On the contrary, there are many examples of such sentences in contemporary professional (e.g. legal) texts. Many examples of semantic similarities that Bobzien presents are based only on the similarities between isolated concepts; however, that is regularly the case for such concepts with the same conceptual basis. Bobzien presents a significant number of matches only on the basis of results that could allegedly be inferred from the texts. However, this cannot be considered a proof of plagiarism. Bobzien does not consider many sources for the continuity of interpretation such as the so-called hypothetical syllogism found in available textbooks of logic. Last but not least, her claims do not consider many differences between Stoic and Frege's logic. All this leads us to the conclusion that Bobzien does not present sufficient facts and connections between them that would confirm her hypothesis about Frege's plagiarism of the Stoic logic: Frege simply was not a plagiarist. [ABSTRACT FROM AUTHOR]

In Berto's logic for aboutness in imagination, the output content of an imaginative episode must be part of the initial content of the episode (Berto, Philos Stud 175:1871–1886, 2018). This condition predicts expressions of perfectly legitimate imaginative episodes to be false. Thus, this condition is too strict. Relaxing the condition to correctly model these cases requires to consider a language with predicates and constants. The paper extends Berto's semantics for aboutness in imagination to a semantics for such a language. The new semantics models contents of formulas along the lines of Hawke's issue-based theory of topics (Hawke, Australas J Philos 96:697–723, 2017), while remaining faithful to the (in)validities discussed by Berto. Several relations between issues and topics are defined, which allow to overcome shortcomings of Hawke's initial framework. These relations are then discussed with respect to their usefulness in the truth condition for the imagination operator. [ABSTRACT FROM AUTHOR]

Partial quasiary predicates are used in programming for representing program semantics and in logic for formalizing predicates over partial variable assignments. Such predicates do not have fixed arity therefore they may be treated as mappings over partial data. Obtained logics are not expressive enough to construct sound axiomatic systems of Floyd--Hoare type. To increase expressibility of such logics, oriented on quasiary predicates, we extend their language with the complement operation (composition). In the paper we define one of such logics called first-order logic of partial quasiary predicates with the complement composition. For this logic a special consequence relation called irrefutability consequence relation under undefinedness conditions is introduced. We study its properties, construct a sequent calculus for it and prove soundness and completeness of this calculus.

In this article, I build an actantial model, M , of John Cage's 1962 indeterminate work 0 ′ 00 ′ ′ (4 ′ 33 ′ ′ No. 2). To further investigate Greimas' actantial axes of desire, knowledge and power, I generate an ontology, O , that records the facts of the model through hierarchies of relations and concepts. This allows for a conceptual graph (CG), C , that describes the score's instructions and its actants. Extracting subgraphs of C then allows for reasoned arguments about the implications of Cage's instructions in the score, and in particular, the composer's reference to "an obligation to others." Through a conceptual graph rule R , I offer a framework for generating the structure of a score-informed interpretation of 0 ′ 00 ′ ′ (4 ′ 33 ′ ′ No. 2) that is based on a number of key conditionals that map the actants of the piece and their relation to the unfolding of the work's narrative. [ABSTRACT FROM AUTHOR]

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation.