Nonmonotonic Reasoning Research Articles

Optimizing the computation of overriding in [formula omitted

One of the factors that is hindering the adoption of nonmonotonic description logics in applications is performance. Even when monotonic and nonmonotonic inferences have the same asymptotic complexity, the implementation of nonmonotonic reasoning may be significantly slower. This happens also with the family of nonmonotonic logics DLN.In this work we address this issue by introducing two optimizations for reasoning in DLN. The first optimization, called optimistic evaluation, aims at exploiting incremental reasoning in a better way. The second is a module extractor forDLN, that has the purpose of focusing reasoning on a relevant subset of the knowledge base. The proposed optimization iterates the module extractor that, unlike classical module extractors, is not idempotent, in general.We prove that the proposed optimizations are correct and complete, and assess them through extensive experiments. Our results prove that optimized DLN reasoning is often compatible with interactive query answering, which brings nonmonotonic description logics closer to practical applications.

Semantic Reasons

AbstractAn analysis of a predicate normally takes the form of a condition that is both necessary and sufficient for the predicate's application. Here I consider the idea, due originally to Friedrich Waismann, that semantic analyses might include conditions that are defeasible, and so allow for exceptions. Analyses of this sort can be expressed in nonmonotonic logic, a post‐Waismann development. I'll argue that defeasibility makes analysis tractable, without making it trivial. I'll also show that a defeasible account of vague predicates can predict our intuitions about particular cases (for instance, that a seven‐foot person counts as tall) without drawing artificial boundaries.

Equivalence in Argumentation Frameworks with a Claim-Centric View – Classical Results with Novel Ingredients

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration are claim-augmented argumentation frameworks (CAFs) which provide a formal basis to analyze conclusion-oriented problems in argumentation by adapting a claim-focused perspective. CAFs extend Dung AFs by associating a claim to each argument representing its conclusion. In this paper, we investigate both ordinary and strong equivalence in CAFs. Thereby, we take the fact into account that one might either be interested in the actual arguments or their claims only. The former point of view naturally yields an extension of strong equivalence for AFs to the claim-based setting while the latter gives rise to a novel equivalence notion which is genuine for CAFs. We tailor, examine and compare these notions and obtain a comprehensive study of this matter for CAFs. We conclude by investigating the computational complexity of naturally arising decision problems.

A semantic approach to nonmonotonic reasoning: Inference operations and choice

AbstractThis paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences frominfinitesets of premisses. The semantics is formulated in terms ofselection functionsand is a generalisation of thepreferential semanticsof Shoham, Kraus et al., and Makinson. A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A proposition is anonmonotonic consequenceof a set of propositions iff holds in all the most preferred ‐states. In the literature on revealed preference theory, there are a number of well‐known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilised here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection,infinitary belief revision operations,that allow for the revision of a theory with a possibly infinite set of propositions, are introduced and characterised axiomatically. Several semantic representation theorems are proved for operations of this kind.

Introduction toStenLindström's “A semantic approach to nonmonotonic reasoning: Inference operations and choice”

Introduction to<scp>S</scp>ten<scp>L</scp>indström's “A semantic approach to nonmonotonic reasoning: Inference operations and choice”

Fidel Semantics for Propositional and First-Order Version of the Logic of CG’3

Paraconsistent extensions of 3-valued Gödel logic are studied as tools for knowledge representation and nonmonotonic reasoning. Particularly, Osorio and his collaborators showed that some of these logics can be used to express interesting nonmonotonic semantics. CG’3 is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG’3 by means of Fidel structures, named CG’3-structures. These structures are constructed from enriched Boolean algebras with a special family of sets. Moreover, we also show that the most basic CG’3-structures coincide with da Costa–Alves’ bi-valuation semantics; this connection is displayed through a Representation Theorem for CG’3-structures. By contrast, we show that for other paraconsistent logics that allow us to present semantics through Fidel structures, this connection is not held. Finally, Fidel semantics for the first-order version of the logic of CG’3 are presented by means of adapting algebraic tools.

Qualitative Mechanical Problem-Solving by Artificial Agents:

&#x0D; &#x0D; &#x0D; Qualitative mechanical problem-solving (QMPS) is central to human-level intelligence. Human agents use their capacity for such problem-solving to succeed in tasks as routine as opening the tap to drink or hanging a picture on the wall, as well as for more sophisticated tasks in demanding jobs in today’s economy (e.g., emergency medicine, plumbing, hydraulic machinery, &amp; driving). Unfortunately, artificial agents (including specifically robots) of today lack the capacity in question. Our work takes QMPS to fall under the general, longstanding AI area of qualitative reasoning (QR), historically an intensely logic-based affair. We embrace this history, and take new, further steps to advance QMPS. The Bennett Mechanical Comprehension Tests (BMCT-I and BMCT-II) assess a human’s ability to solve QMPS problems, and are used in the real world by many employers to evaluate job candidates. Building on the work of others who have attacked BMCT under the rubric of Psychometric AI (PAI), we introduce one of our novel algorithms (A_B1) in a family (A_B) of such for QMPS as required by BMCT, illustrate via case studies, report time-based performance of A_B1, and assess our progress with an eye to future work in which our approach is extended to a sub-class of algorithms in A_B that exploit the power of argument-based nonmonotonic logic, and leverage the success of transformer models to enhance their efficiency.&#x0D; &#x0D; &#x0D;

A SIMPLE SEQUENT SYSTEM FOR MINIMALLY INCONSISTENT LP

AbstractMinimally inconsistent LP (MiLP) is a nonmonotonic paraconsistent logic based on Graham Priest’s logic of paradox (LP). Unlike LP, MiLP purports to recover, in consistent situations, all of classical reasoning. The present paper conducts a proof-theoretic analysis of MiLP. I highlight certain properties of this logic, introduce a simple sequent system for it, and establish soundness and completeness results. In addition, I show how to use my proof system in response to a criticism of this logic put forward by J. C. Beall.

„Defeasible Reasoning“ und die Fragmentierung der deontischen Logik

My contribution starts with an analysis of the structure of normative argumentation, which is understood as the balancing of normative arguments that leads to normative judgements. Its crucial point is that normative arguments and normative judgements have distinct logical structures, and that normative judgements do not follow logically from a set of premises, but result from an act of judgement. Based on this analysis, three theses are advanced: The Inadequacy thesis, stating that neither deductive nor nondeductive (non-monotonic) logic provides an adequate account for the reasoning with conflicting normative arguments. The Fragmentation thesis, suggesting that deontic logic should be developed as a formal characterization of diverse notions of validity of norms and hence there is no single deontic logic. The Deductivity thesis, claiming that normative reasoning from the internal point of view of someone making normative judgements is in its core deductive, and non-monotonic or defeasible reasoning is, from this perspective, merely a deficient form of reasoning. Finally, it is asked what might be a field of application of defeasible reasoning in the field of legal argumentation, and a suggestion is made regarding the notion of defeasibility.

IMSD: Interactive Methods for Finding Similar or Diverse Answer Sets

Answer set programming (ASP) is a modeling language in knowledge representation, rooted in Logic Programming and Nonmonotonic Reasoning, which has been gaining increasing attention during the last years. In recent years, many of the researchers developed integrated development environments (IDE) for ASP programs including editors and debuggers. Other researchers focused on analyzing the answer sets, they introduced offline and online methods to find specific solutions of a given problem in answer set programming in different approaches such as phylogeny reconstruction. However, with an enormous number of answer sets could be available, the user is not interested in all of them. Thus, a navigation of the search space could be a solution to help the user to access the specific answer sets. To this end, we aim at finding similar/diverse solutions of the answer sets with a new method. The intuition behind this navigation is to make the search faster than other methods and explore information that is related to the user’s query. Afterward, we implement a tool performing the above approach in order to simplify the search task and show the applicability and effectiveness of our method. We conclude by testing the performance of the proposed tool into a real-world example of ASP programs.

IMSD: Interactive Methods for Finding Similar or Diverse Answer Sets

Answer set programming (ASP) is a modeling language in knowledge representation, rooted in Logic Programming and Nonmonotonic Reasoning, which has been gaining increasing attention during the last years. In recent years, many of the researchers developed integrated development environments (IDE) for ASP programs including editors and debuggers. Other researchers focused on analyzing the answer sets, they introduced offline and online methods to find specific solutions of a given problem in answer set programming in different approaches such as phylogeny reconstruction. However, with an enormous number of answer sets could be available, the user is not interested in all of them. Thus, a navigation of the search space could be a solution to help the user to access the specific answer sets. To this end, we aim at finding similar/diverse solutions of the answer sets with a new method. The intuition behind this navigation is to make the search faster than other methods and explore information that is related to the user’s query. Afterward, we implement a tool performing the above approach in order to simplify the search task and show the applicability and effectiveness of our method. We conclude by testing the performance of the proposed tool into a real-world example of ASP programs.

Nonmonotonic reasoning from conditional knowledge bases with system W

For nonmonotonic reasoning in the context of a knowledge base mathcal {R} containing conditionals of the form If A then usually B, system P provides generally accepted axioms. Inference solely based on system P, however, is inherently skeptical because it coincides with reasoning that takes all ranking models of mathcal {R} into account. System Z uses only the unique minimal ranking model of mathcal {R}, and c-inference, realized via a complex constraint satisfaction problem, takes all c-representations of mathcal {R} into account. C-representations constitute the subset of all ranking models of mathcal {R} that are obtained by assigning non-negative integer impacts to each conditional in mathcal {R} and summing up, for every world, the impacts of all conditionals falsified by that world. While system Z and c-inference license in general different sets of desirable entailments, the first major objective of this article is to present system W. System W fully captures and strictly extends both system Z and c-inference. Moreover, system W can be represented by a single strict partial order on the worlds over the signature of mathcal {R}. We show that system W exhibits further inference properties worthwhile for nonmonotonic reasoning, like satisfying the axioms of system P, respecting conditional indifference, and avoiding the drowning problem. The other main goal of this article is to provide results on our investigations, underlying the development of system W, of upper and lower bounds that can be used to restrict the set of c-representations that have to be taken into account for realizing c-inference. We show that the upper bound of n − 1 is sufficient for capturing c-inference with respect to mathcal {R} having n conditionals if there is at least one world verifying all conditionals in mathcal {R}. In contrast to the previous conjecture that the number of conditionals in mathcal {R} is always sufficient, we prove that there are knowledge bases requiring an upper bound of 2n− 1, implying that there is no polynomial upper bound of the impacts assigned to the conditionals in mathcal {R} for fully capturing c-inference.

Nonmonotonic Reasoning, Expectations Orderings, and Conceptual Spaces

In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.

The Co-Constructed Logic Framework for Understanding Children’s Acts and Their Intentions

With the characteristics of the nonmonotonic logic and defeasible inference, abductive reasoning has been formalized in the field of artificial intelligence, dealing with the local pragmatics (e.g., the resolution of coreference, resolving syntactic and lexical ambiguity and interpreting metonymy and metaphor), recognizing discourse structure and even the speaker’s plan and other issues for natural language understanding. However, Hobbs’ analysis of abduction in recognizing the speaker’s plan was conducted only from the point of view of the verbal information processing that the listener does. To demonstrate the collaborative way that conversational partners working together to understand the logic of human acts and their intentions, this article analyzes the two conversations about the parents questioning their children’s intention for their acts with an abductive reasoning method. The results show that children and parents co-construct segments of discourse with coherence relations across several conversational turns, by that way they build together a simplified framework for understanding the logic of human acts and their intention. For example, when the father and his children co-constructed coherent segments of discourse with the result relation between them, they completed the particular intention understanding at the same time. This research helps in enriching the logic structure of artificial intelligence applications such as visual question answering models and enhancing their reasoning abilities.

FOLASP: FO(·) as Input Language for Answer Set Solvers

AbstractTechnological progress in Answer Set Programming (ASP) has been stimulated by the use of common standards, such as the ASP-Core-2 language. While ASP has its roots in nonmonotonic reasoning, efforts have also been made to reconcile ASP with classical first-order (FO) logic. This has resulted in the development of FO(·), an expressive extension of FO, which allows ASP-like problem solving in a purely classical setting. This language may be more accessible to domain experts already familiar with FO and may be easier to combine with other formalisms that are based on classical logic. It is supported by the IDP inference system, which has successfully competed in a number of ASP competitions. Here, however, technological progress has been hampered by the limited number of systems that are available for FO(·). In this paper, we aim to address this gap by means of a translation tool that transforms an FO(·) specification into ASP-Core-2, thereby allowing ASP-Core-2 solvers to be used as solvers for FO(·) as well. We present experimental results to show that the resulting combination of our translation with an off-the-shelf ASP solver is competitive with the IDP system as a way of solving problems formulated in FO(·).

Ensuring reference independence and cautious monotony in abstract argumentation

In the symbolic artificial intelligence community, abstract argumentation with its semantics, i.e. approaches for defining sets of valid conclusions (extensions) that can be derived from argumentation graphs, is considered a promising method for non-monotonic reasoning. However, from a sequential perspective, abstract argumentation-based decision-making processes typically do not guarantee an alignment with common formal notions to assess consistency; in particular, abstract argumentation can, in itself, not enforce the satisfaction of relational principles such as reference independence (based on a key principle of microeconomic theory) and cautious monotony. In this paper, we address this issue by introducing different approaches to ensuring reference independence and cautious monotony in sequential argumentation: a reductionist, an expansionist, and an extension-selecting approach. The first two approaches are generically applicable, but may require comprehensive changes to the corresponding argumentation framework. In contrast, the latter approach guarantees that an extension of the corresponding argumentation framework can be selected to satisfy the relational principle by requiring that the used argumentation semantics is weakly reference independent or weakly cautiously monotonous, respectively, and also satisfies some additional straightforward principles. To highlight the relevance of the approach, we illustrate how the extension-selecting approach to reference independent argumentation can be applied to model (boundedly) rational economic decision-making.

Autonomous Decision-Making With Incomplete Information and Safety Rules Based on Non-Monotonic Reasoning

In this article we propose a decision process integrating Non-Monotonic Reasoning (NMR), embedded in a deliberative architecture. The NMR process uses Default Logic to implement goal reasoning, managing partially observable or incomplete information, allowing the design of default behaviours completed by the handling of specific situations, in order to manage the current mission objective as well as safety rules. We illustrate our approach through an application of an underwater robot performing a marine biology mission.

Combining Probabilistic Planning and Logic Programming on Mobile Robots

Key challenges to widespread deployment of mobile robots to interact with humans in real-world domains include the ability to: (a) robustly represent and revise domain knowledge; (b) autonomously adapt sensing and processing to the task at hand; and (c) learn from unreliable high-level human feedback. Partially observable Markov decision processes (POMDPs) have been used to plan sensing and navigation in different application domains. It is however a challenge to include common sense knowledge obtained from sensory or human inputs in POMDPs. In addition, information extracted from sensory and human inputs may have varying levels of relevance to current and future tasks. On the other hand, although a non-monotonic logic programming paradigm such as Answer Set Programming (ASP) is wellsuited for common sense reasoning, it is unable to model the uncertainty in real-world sensing and navigation (Gelfond 2008). This paper presents a hybrid framework that integrates ASP, hierarchical POMDPs (Zhang and Sridharan 2012) and psychophysics principles to address the challenges stated above. Experimental results in simulation and on mobile robots deployed in indoor domains show that the framework results in reliable and efficient operation.

Fixpoint Semantics for Recursive SHACL

SHACL is a W3C-proposed language for expressing structural constraints on RDF graphs. The recommendation only specifies semantics for non-recursive SHACL; recently, some efforts have been made to allow recursive SHACL schemas. In this paper, we argue that for defining and studying semantics of recursive SHACL, lessons can be learned from years of research in non-monotonic reasoning. We show that from a SHACL schema, a three-valued semantic operator can directly be obtained. Building on Approximation Fixpoint Theory (AFT), this operator immediately induces a wide variety of semantics, including a supported, stable, and well-founded semantics, related in the expected ways. By building on AFT, a rich body of theoretical results becomes directly available for SHACL. As such, the main contribution of this short paper is providing theoretical foundations for the study of recursive SHACL, which can later enable an informed decision for an extension of the W3C recommendation.

Penalty Logic: Paraconsistency and Applications

Penalty logic is a non-classical non-monotonic logic which allows us to demonstrate the power of belief, the level of truth or the reliability of data that we are using. This logic can be useful to model human reasoning or to replace the penalty function in the sphere of Machine Learning. We can also talk about paraconsistency of this logic and suggest the definition of contradiction without negation.