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InfOCF-Web provides implementations of system P and system Z inference, and of inference relations based on c-representation with respect to various inference modes and different classes of minimal models. It has an easy-to-use online interface for computing ranking models of a conditional knowledge R, and for answering queries and comparing inference results of nonmonotonic inference relations induced by R.

The exact relationship between formal argumentation and nonmonotonic logics is a research topic that keeps on eluding researchers despite recent intensified efforts. We contribute to a deeper understanding of this relation by investigating characterizations of abstract dialectical frameworks in conditional logics for nonmonotonic reasoning. We first show that in general, there is a gap between argumentation and conditional semantics when applying several intuitive translations, but then prove that this gap can be closed when focusing on specific classes of translations., Annals of mathematics and artificial intelligence;Bd 89. 2021, H. 10/11, S. 1075-1099

The article aims to show how the acceptance of non-monotonic logic enables arguments to be held between science and religion in a way that does not exclude either of these two spheres. The starting point of the analyses is the idea of the 13th century Danish philosopher, Boethius of Dacia, who states that it is both acceptable that: (1) a natural scientist negates that the world had a beginning, and (2) a Christian theologian asserts that the world had a beginning, because each of them is basing their statements on the principles of their respective discipline: the first on the principles of nature, and the latter on knowledge supplemented by divine revelation. What is more, analogically: (3) a metaphysician, when limited to his principles, cannot settle the issue, as he takes into account supranatural beings and their powers, but cannot know what God or another powerful supranatural would have decided in a such a case. The paper shows that Boethius’s approach: (1) violates the rule of monotonicity, (2) cannot be finally interpreted in terms of classical logic and (3) assumes certain non-monotonic logic as its inference framework. Other presented examples of arguments between religious beliefs and the statements of natural science are resolved in the same way. Thus, it is shown how non-monotonic thinking allows us to seriously treat both scientific and religious inference as compatible.

Pavel Florensky (1882–1937), a Russian theologian, philosopher, and mathematician, argued that the religious discourse is essentially contradictory and put forward the idea of the logical theory of antinomies. Recently his views raised interesting discussions among logicians who consider him a forerunner of many non-classical logics. In this paper I discuss four interpretations of Florensky’s views: paraconsistent, L-contradictory, non-monotonic and rhetorical. In conclusion I argue for the integral interpretation which unites these four approaches.

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe E L O ⊥ , a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe E L O ⊥ under RC that relies entirely on a series of classical, monotonic E L ⊥ subsumption tests. Therefore, any existing classical monotonic E L ⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.

We introduce a logic for knowledge representation and reasoning on protein-protein interactions. Modulo a theory, formulas describe protein structures and dynamic changes. They can be composed in order to add or remove static and dynamic observations. A second-order circumscription operator then enables nonmonotonic reasoning on the changes implied by a formula. We introduce deduction rules that produce formulas which are, up to equivalence, in a first-order fragment with decidable satisfiability and validity. Importantly, the rules can produce circumscribed formulas., Comment: In Proceedings ICLP 2019, arXiv:1909.07646

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/\textsc{dlv} for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the \textsc{dlv} system, and tested for ontological reasoning, confirming their effectiveness. Under consideration for publication in Theory and Practice of Logic Programming., Comment: Paper presented at the 35th International Conference on Logic Programming (ICLP 2019), Las Cruces, New Mexico, USA, 20-25 September 2019, 16 pages

Rational closure is one of the most extensively studied nonmonotonic extensions of description logics. Nonetheless, so far it has been investigated only for description logics that satisfy the disjoint model union property, or limited fragments that support nominals. In this paper we show that for sufficiently expressive description logics, the traditional correspondence between rational closure and ranked interpretations does not hold. Therefore, in order to extend rational closure to a wider class of description logics it is necessary to change the definition of rational closure, or alternatively abandon its standard semantics. Here we pursue the former approach, and introduce stable rational closure, based on stable rankings. The resulting nonmonotonic logic is a natural extension of the standard rational closure: First, its refined exceptionality criterion yields a closure that satisfies the KLM postulates. Second, when a knowledge base enjoys the disjoint model union property, then stable rational closure equals the old notion. In the other cases, stable rankings may raise the exceptionality level of some concepts. Stable rational closure has a model-theoretic semantics based on upward-closed models, that relax the canonical models adopted in the past, in order to deal with logics that do not satisfy the disjoint union model property. Unfortunately, stable rankings do not always exist, and are not necessarily unique. However, they can be effectively enumerated for all defeasible knowledge bases in SROIQ , using any algorithm for reasoning with ranked models.

In this paper we present a duality between nonmonotonic consequence relations and well-founded convex geometries. On one side of the duality we consider nonmonotonic consequence relations satisfying the axioms of an infinitary variant of System P, which is one of the most studied axiomatic systems for nonmonotonic reasoning, conditional logic and belief revision. On the other side of the duality we consider well-founded convex geometries, which are infinite convex geometries that generalize well-founded posets. Since there is a close correspondence between nonmonotonic consequence relations and path independent choice functions one can view our duality as an extension of an existing duality between path independent choice functions and convex geometries that has been developed independently by Koshevoy and by Johnson and Dean.

We introduce a nonmonotonic procedure for preferential Description Logics in order to reason about typicality by taking probabilities of exceptions into account. We consider an extension, called ALC + T R P , of the logic of typicality ALC + T R by inclusions of the form T ( C ) ⊑ p D with probability p, whose intuitive meaning is that “all the typical Cs are Ds, and the probability that a C is not a D is 1 − p ”. We consider a notion of extension of an ABox containing only some typicality assertions, then we equip each extension with a probability. We then restrict entailment of a query F to those extensions whose probabilities belong to a given and fixed range. We propose a decision procedure for reasoning in ALC + T R P and we exploit it to show that entailment is ExpTime -complete as for the underlying ALC .

Efforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanatio...

We study the complexity of the inference problem for propositional circumscription (the minimal inference problem) over arbitrary finite domains. The problem is of fundamental importance in nonmonotonic logics and commonsense reasoning. The complexity of the problem for the two-element domain has been completely classified. In this article, we classify the complexity of the problem over all conservative languages. We consider a version of the problem parameterized by a set of relations (a constraint language), from which we are allowed to build a knowledge base, and where a linear order used to compare models is a part of an input. We show that in this setting the problem is either Π P 2 -complete, coNP-complete, or in P. The classification is based on a coNP-hardness proof for a new class of languages, an analysis of languages that do not express any member of the class, and a new general polynomial-time algorithm solving the minimal inference problem for a large class of languages.

This article presents results from a simulation-based study of inheritance inference, that is, inference from the typicality of a property among a "base" class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of "exceptional subclasses" (i.e., subclasses that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses.

In order to characterize causal relation, different scholars have studied it from multiple perspectives. In the field of logic, the causal theory proposed by Alexander elaborated the causal relationship from the perspective of nonmonotonic reasoning. The Horn causal theory and the concept of equivalence relationship are defined in his article, but the author did not give the determination method of equivalence relationship. In order to make up for this deficiency, this paper introduces the concept of bisimulation to describe the equivalence relation between Horn causal theories and proves the consistency between bisimulation relation and the equivalence of models. Then the corresponding algorithm is proposed to determine the equivalence. An example is also given to illustrate the application of this method in determining equivalence relationship.

An important concept for nonmonotonic reasoning in the context of a conditional belief base \(\mathcal R\) is syntax splitting, essentially stating that taking only the syntactically relevant part of \(\mathcal R\) into account should be sufficient. In this paper, for the semantics of ordinal conditional functions (OCF) of \(\mathcal R\), we introduce the notion of semantic splitting of \(\mathcal R\) where the combination of models of sub-belief bases of \(\mathcal R\) corresponds to the models of \(\mathcal R\). While this is not the case for all OCF models, we show that for c-representations which are a subclass of all OCFs governed by the principle of conditional preservation, every syntactic splitting is also a semantic splitting. Furthermore, for the semantics of c-representations, we introduce constraint splittings of a conditional belief base and show that they fully capture and go beyond syntax splittings, thus allowing for additional belief base splittings that enable the computation of models locally from sub-belief bases.

Most (if not all) nonmonotonic logics are assumed to be cumulative, which is often regarded as the minimum requirement for a logic. We argue that cumulativity, in particular, cumulative transitivity can be abandoned, in order to better characterize reasoning in uncertainty. But giving up cumulative transitivity makes it hard to obtain representation results for these logics. Borrowing the idea from strict-tolerant logics, we give some representation results for nonmonotonic logics that are not cumulatively transitive.

This article defines a family of inference relations which aim at reasoning with inconsistent knowledge bases. These inference relations are defined out of inconsistency measures. We check under which conditions the new inference relations satisfy a series of properties for nonmonotonic reasoning. We also show that they are paraconsistent when the corresponding inconsistency measures satisfy some rationality postulates. Besides, we show some dependencies and incompatibilities among some rationality postulates.

We propose a novel formal framework (called 3D-nCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-nCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and nCDC-ASP to 3D. 3D-nCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-nCDC-ASP, and illustrate its usefulness with applications. This paper is under consideration for acceptance in TPLP., Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 29 pages, 6 figures

The propositional logic Lp is the smallest syntax that formalizes Aristotle's three principles. It is commonly accepted that it is insufficient to capture human reasoning. Many formalisms have been proposed to extend the modeling capabilities of formal languages. The most common approach is to extend or to impoverish the syntax of Lp. We propose, with the contextual logic Lc, to take a different path. It consists in automatically integrating into the set of atomic propositions of the language silent propositions, which we call thoughts. By identifying the formulae, they bring to the formalism a reflexive reasoning capacity. We use it to define a semantic interpretation function of models, which captures the notions of inconsistency and predicate. The contribution of Lc to the family of non-classical formalisms is that it models fallibilistic reasoning (an intelligent agent has no certainty and believes what seems justifiable to him) and perspectivist reasoning (his beliefs are obtained by summing up the beliefs he has from several disjoint perspectives). We illustrate the behavioral properties of the contextual logic by developing at length an example of application. It allows us to present how to use it in the framework of Symbolic Artificial Intelligence.; La logique propositionnelle Lp est la plus petite syntaxe qui formalise les trois principes d'Aristote. Il est communément admis qu'elle est insuffisante pour capturer le raisonnement humain. De nombreux formalismes ont été proposés pour étendre les capacités de modélisation des langages formels. L’approche la plus souvent étudiée consiste à étendre ou à appauvrir la syntaxe de Lp. Nous proposons, avec la logique contextuelle Lc, d'emprunter une voie différente. Elle consiste à intégrer automatiquement dans l'ensemble des propositions atomiques du langage des propositions silencieuses, que nous appelons des pensées. En identifiant les formules, elles apportent au formalisme une capacité de raisonnement réflexif. Nous l'utilisons pour définir une fonction d’interprétation sémantique sur les modèles, qui capture les notions d'inconsistance et de prédicat. L’apport de Lc à la famille des formalismes non-classiques est qu'elle modélise le raisonnement faillibiliste (un agent intelligent n'a aucune certitude et croit ce qui lui semble justifiable) et le raisonnement perspectiviste (ses croyances sont obtenues en additionnant les croyances qu'il a de plusieurs perspectives disjointes). Nous illustrons les propriétés comportementales de la logique contextuelle en développant longuement un exemple d'application. Il nous permet de présenter comment l'utiliser dans le cadre de l'Intelligence Artificielle Symbolique.

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs ukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

The aim of the present chapter is to overview three important tools for knowledge representation that are strongly interrelated. All three can be traced back to a fundamental limitation of classical logic: its connectives are truth-functional, which does not allow to reason about some concepts such as modalities and “if-then” relationships between propositions. To witness, most of the students in an introductory course on logic have a hard time to accept that the implication “if A then B” should be identified with “A is false or B is true”. Indeed, such an identification leads to validities that are rather counter-intuitive, such as “B implies A implies B” or “A implies B, or B implies A”. In introductory courses it is often omitted that the above interpretation of the so-called material implication was subject of much concern among scholars in the past. Their work led to the development of several families of formalisms that will be presented in this chapter: modal logics, conditional logics, and nonmonotonic formalisms. The next three sections detail the definitions of each of these: the modal logics K and S5, the conditional logics due to Stalnaker and Lewis, and the preferential and rational nonmonotonic reasoning formalisms. We then study the relationship between conditional logics and dynamic epistemic logics. The latter are a family of modal logics that got popular recently. We show that they can be viewed as particular logics of indicative conditionals: they are in the Stalnaker family and violate all of Lewis’s principles.

We focus on understanding natural language (NL) definitions of new entities via the ones available in the current version of an ontology. Once a definition is acquired from a user or from documents, this and other users can rely on the newly defined entity to formulate new questions. We first explore how to automatically build a taxonomy from a corpus of documents or from the web, and use this taxonomy to filter out irrelevant answers. We then develop a logical form approach to building definitions from text and outline an algorithm to build a step-by-step definition representation that is consistent with the current ontology. A nonmonotonic reasoning-based method is also proposed to correct semantic representations of a query. In addition, we focus on a special case of definitions such as NL descriptions of algorithm for the NL programming paradigm. Finally, search relevance improvement is evaluated based on acquired taxonomy and ontology.

ASPIC+ is an established general framework for argumentation and non-monotonic reasoning. However, ASPIC+ does not satisfy the non-contamination rationality postulates, and moreover, tacitly assumes unbounded resources when demonstrating satisfaction of the consistency postulates. In this paper we present a new version of ASPIC+ – Dialectial ASPIC+ – that is fully rational under resource bounds.

Abductive and counterfactual reasoning, core abilities of everyday human cognition, require reasoning about what might have happened at time t, while conditioning on multiple contexts from the relative past and future. However, simultaneous incorporation of past and future contexts using generative language models (LMs) can be challenging, as they are trained either to condition only on the past context or to perform narrowly scoped text-infilling. In this paper, we propose DeLorean, a new unsupervised decoding algorithm that can flexibly incorporate both the past and future contexts using only off-the-shelf, left-to-right language models and no supervision. The key intuition of our algorithm is incorporating the future through back-propagation, during which, we only update the internal representation of the output while fixing the model parameters. By alternating between forward and backward propagation, DeLorean can decode the output representation that reflects both the left and right contexts. We demonstrate that our approach is general and applicable to two nonmonotonic reasoning tasks: abductive text generation and counterfactual story revision, where DeLorean outperforms a range of unsupervised and some supervised methods, based on automatic and human evaluation., EMNLP 2020

Different approaches have been investigated for the modelling of real-world situations, especially in the medical field, many of which are based on probabilities or other numerical parameters. In this paper, we show how real world situations from the biomedical domain can be conveniently modelled with qualitative conditionals by presenting three case studies: modelling the classification of certain mammals, modelling infections with the malaria pathogen, and predicting the outcome of chronic myeloid leukaemia. We demonstrate that the knowledge to be modelled can be expressed directly and declaratively using qualitative conditional logic. For instance, it is straightforward to handle exceptions to a general rule as conditionals support nonmonotonic reasoning. Each of the knowledge bases is evaluated with example queries and with respect to different inference mechanisms that have been proposed for conditional knowledge, including p-entailment, system Z, and various inference relations based on c-representations. Comparing the obtained inference results with the answers expected from human experts demonstrates the feasibility of the modelling approach and also provides an empirical evaluation of the employed nonmonotonic inference relations in realistic application scenarios.

Answer Set Programming (ASP) is a rule-based language rooted in traditional Logic Programming, Databases, Knowledge Representation, and Nonmonotonic Reasoning. It offers a flexible language for declarative problem solving, with support of efficient general-purpose solvers and reasoners. The larger part of this article provides an introduction to ASP, with a historical perspective, a definition of the core language, a guideline to knowledge representation, and an overview of existing ASP solvers. One part focuses on one commonly used feature: aggregates and generalized atoms. The inclusion of aggregates in ASP (and Logic Programming at large) has long been motivated, however there are some issues with semantics to be addressed, in particular when aggregates occur in recursive definitions. Very similar considerations are needed when coupling ASP with other formalisms, which we collectively refer to as “generalized atoms”. An overview of these semantic challenges and proposals for addressing them is provided, along with an overview of complexity results and system support.

Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.

@article{dung:aij95, author ="P. Dung", title=" and its fundamental role in non-monotonic reasoning, logic programming and n

Considered are the questions of designing a system for modeling the reasoning of a cognitive agent, capable of making conclusions based on its knowledge and observations of the external environment, solving problems in a hard enough real-time mode. To work in this mode, the existence of a critical time threshold is established, which is set to solve the problem facing the agent. Exceeding the threshold is fraught with grave, sometimes catastrophic consequences and for the agent is unacceptable. The formal basis of the modeling system (cognitive process control) is a logical system - extended step theory, that combines the concepts of active temporal logic and logical programming. Among the original methods proposed by the authors in the work, an approach to combining the concepts of active logic and logical programming in one logical system should be noted; an approach to constructing a consistent declarative semantics for extended step theory of active logic; a method of formalizing temporal, nonmonotonic reasoning of an agent using extended step theory of active temporal logic; a method of granulating time in a logical system to formalize meta-reasoning. A subclass of temporal logic is considered, oriented to application in real-time systems. Additionally, the issues of managing the agent’s cognitive process in hard real-time, eliminating anomalies (unforeseen situations), and applying the temporal logic of branching time are investigated in more detail.

Logic is the foundation of AI, and the majority of AI’s principles are based on logical or deductive reasoning. The chapter presents: contributions of pioneers of logic, the argumentation theory, which is based on logic and with its roots in propositional logic, the process of validating the propositional formulas, their syntax and semantics, interpretation of a logical expression through semantic tableau, followed with presents the basic reasoning patterns used by human, and their formal notations. In addition, presents the normal forms of propositional formulas and application of resolution principle on these for inference. The nonmonotonic reasoning and its significance is briefly described. At the end, the chapter presents the axiomatic system due to Hilbert and its limitations, and concludes with chapter summary.

This chapter addresses the main approaches to formalization of default reasoning in first-order framework. The first part of the chapter overviews the historical development of nonmonotonic reasoning systems. After discussing three wellknown early formalisms (Default Logic, Nonmonotonic modal logic and Circumscription), we focus on nonmonotonic consequence relations and their close connections with conditional logics and probabilistic reasoning systems. The logic \( \mathit L ^{P,\mathbb I}_{\mathit \omega\omega}\) ww occupies the central position in this chapter. This logic extends classical first-order logic with a list of Keisler-style conditional probability quantifiers with the intention to express statistical knowledge as well as approximate probabilities. We provide a sound and complete deductive system with respect to semantics based on first-order structures endowed with suitable probability spaces. In addition, we describe two decidable fragments of \( \mathit L ^{P,\mathbb I}_{\mathit \omega\omega}\) ww that seem to be rich enough for many practical purposes. Finally, we discuss how the logic \( \mathit L ^{P,\mathbb I}_{\mathit \omega\omega}\) ww and its suitable extensions can be used to model default reasoning and analyze some properties of nonmonotonic consequence relations in the light of probabilistic inference.

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (\(\mathsf {LAN}\)) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging \(\mathsf {LAN}\), we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the three categories and evaluate their validity vis-a-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property.

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka's framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic EL+bot. The paper is under consideration for acceptance in TPLP., Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020

Answer Set Programming (ASP) is a well-known declarative problem solving approach based on nonmonotonic logic programs, which has been successfully applied to a wide range of applications in artificial intelligence and beyond. To address the needs of modern applications, HEX-programs were introduced as an extension of ASP with external atoms for accessing information outside programs via an API style bi-directional interface mechanism. To evaluate such programs, conflict-driving learning algorithms for SAT and ASP solving have been extended in order to capture the semantics of external atoms. However, a drawback of the state-of-the-art approach is that external atoms are only evaluated under complete assignments (i.e., input to the external source) while in practice, their values often can be determined already based on partial assignments alone (i.e., from incomplete input to the external source). This prevents early backtracking in case of conflicts, and hinders more efficient evaluation of HEX-programs. We thus extend the notion of external atoms to allow for three-valued evaluation under partial assignments, while the two-valued semantics of the overall HEX-formalism remains unchanged. This paves the way for three enhancements: first, to evaluate external sources at any point during model search, which can trigger learning knowledge about the source behavior and/or early backtracking in the spirit of theory propagation in SAT modulo theories (SMT). Second, to optimize the knowledge learned in terms of so-called nogoods, which roughly speaking are impossible input-output configurations. Shrinking nogoods to their relevant input part leads to more effective search space pruning. And third, to make a necessary minimality check of candidate answer sets more efficient by exploiting early external evaluation calls. As this check usually accounts for a large share of the total runtime, optimization is here particularly important. We further present an experimental evaluation of an implementation of a novel HEX-algorithm that incorporates these enhancements using a benchmark suite. Our results demonstrate a clear efficiency gain over the state-of-the-art HEX-solver for the benchmarks, and provide insights regarding the most effective combinations of solver configurations.

In nonmonotonic reasoning there are the problems of inconsistency and incoherence in general, and in default reasoning there may be only one trivial extension or no extension in special. We propose the restricted semantics of four-valued logic for default reasoning to resolve the problems of inconsistency and incoherence and in the meantime retain classical extensions in the presence of consistency and coherency. The restricted semantics can maintain both the expressiveness and reasoning ability of default logic. We provide a transformation approach to compute the restricted extensions by reducing them into classical ones.

Alternative logics have been invoked periodically to explain the systematically different modes of thought of the subjects of ethnography: one logic for ‘us’ and another for ‘them’. Recently anthropologists have cast doubt on the tenability of such an explanation of difference. In cognitive science, [Stenning and van Lambalgen, 2008] proposed that with the modern development of multiple logics, at least several logics are required for making sense of the cognitive processes of reasoning for different purposes and in different contexts. Alongside Classical logic (CL) — the logic of dispute), there is a need for a nonmonotonic logic (LP) which is a logic of cooperative communication. Here we propose that all people with various cultural backgrounds make use of multiple logics, and that difference should be captured as variation in the social contexts that call forth the different logics’ application. This contribution illustrates these ideas with reference to the ethnography of divination.

We present a formal argumentation system for dealing with the detachment of prioritized conditional obligations and permissions. In the presence of facts and constraints, we answer the question whether an unconditional obligation or permission is detachable by considering arguments for and against its detachment. For the evaluation of arguments in favour of detachment, we use a Dung-style argumentation-theoretical semantics. We illustrate how violations and contrary-to-duty scenarios are dealt with in our framework and pay special attention to conflict-resolution via priorities.

Issue title: Special Issue on the 30th Italian Conference on Computational Logic: CILC 2015Guest editors: Marco Maratea, Viviana Mascardi, Davide Ancona and Alberto Pettorossi; International audience; We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic SHIQ. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of SHIQ into entailment in SHIQ. We discuss the extension of rational closure to more expressive description logics.

Jorg Hansen, John Horty, and Xavier Parent and Leendert van der Torre have all recently described some sort of nonmonotonic logic to model reasons and their interactions. Horty’s framework is broader in scope than the other two, encompassing both reasoning about the relative strengths of reasons and reasoning about which reasons to consider in the first place. Hansen discusses a plethora of approaches and examples, including Horty’s, arguing that his preferred system best captures our intuitions. And Parent and van der Torre present a family of systems of input/output logic, which are in some ways the most flexible. In this paper, I aim to combine these features. Without attempting to answer the question of which intuitions are the best to capture, I first argue that there are good reasons to explore systems that behave more like Hansen’s than Horty’s. I then show that Parent and van der Torre’s framework of input/output logic can exactly duplicate Hansen’s system but is flexible enough to produce other results as well. Finally, I extend their framework to include the additional kinds of reasoning Horty discusses, showing that the resulting theory can handle a wider range of cases than Horty’s.

Answer Set Programming (ASP) is a well-established paradigm for declarative programming and nonmonotonic reasoning. ASP allows for flexible modeling using rules. ASP rules induce a set of intended models called answer sets. Incoherence, the non-existence of answer sets, is therefore a feature of ASP, indicating that the rules admit no intended models. However, this feature can also be problematic in certain circumstances: errors that cause incoherence are notoriously difficult to debug, and query answering will not provide any meaningful answers for incoherent programs. Paracoherent semantics have been suggested as a remedy. They extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. However, paracoherent semantics have essentially been inapplicable in practice, due to the lack of efficient algorithms and implementations. In this paper, this lack is addressed, and several different algorithms to compute semi-stable and semi-equilibrium models are proposed and implemented within an answer set solving framework. A key role in the framework is played by syntactic program transformations that allow for characterizing paracoherent semantics in terms of the answer sets of transformed programs. Apart from existing transformations from the literature, a novel transformation is also proposed, which provides an alternative characterization of paracoherent semantics in terms of (extended) externally supported models. Notably, the new transformation is more compact than the existing ones, and brings performance benefits. An extensive empirical performance comparison among the algorithms on benchmarks from ASP competitions and a real-world use case is given as well. It shows not only that the methods developed in this paper lead to practically effective systems, but also show a clear advantage of the methods that rely on (extended) externally supported models.