From Logic Programming to Human Reasoning:: How to be Artificially Human

Results of psychological experiments have shown that humans make assumptions, which are not necessarily valid, that they are influenced by their background knowledge and that they reason non-monotonically. These observations show that classical logic does not seem to be adequate for modeling human reasoning. Instead of assuming that humans do not reason logically at all, we take the view that humans do not reason classical logically. Our goal is to model episodes of human reasoning and for this purpose we investigate the so-called Weak Completion Semantics. The Weak Completion Semantics is a Logic Programming approach and considers the least model of the weak completion of logic programs under the three-valued Łukasiewicz logic. As the Weak Completion Semantics is relatively new and has not yet been extensively investigated, we first motivate why this approach is interesting for modeling human reasoning. After that, we show the formal correspondence to the already established Stable Model Semantics and Well-founded Semantics. Next, we present an extension with an additional context operator, that allows us to express negation as failure. Finally, we propose a contextual abductive reasoning approach, in which the context of observations is relevant. Some properties do not hold anymore under this extension. Besides discussing the well-known psychological experiments Byrne’s suppression task and Wason’s selection task, we investigate an experiment in spatial reasoning, an experiment in syllogistic reasoning and an experiment that examines the belief-bias effect. We show that the results of these experiments can be adequately modeled under the Weak Completion Semantics. A result which stands out here, is the outcome of modeling the syllogistic reasoning experiment, as we have a higher prediction match with the participants’ answers than any of twelve current cognitive theories. We present an abstract evaluation system for conditionals and discuss well-known examples from the literature. We show that in this system, conditionals can be evaluated in various ways and we put up the hypothesis that humans use a particular evaluation strategy, namely that they prefer abduction to revision. We also discuss how relevance plays a role in the evaluation process of conditionals. For this purpose we propose a semantic definition of relevance and justify why this is preferable to a exclusively syntactic definition. Finally, we show that our system is more general than another system, which has recently been presented in the literature. Altogether, this thesis shows one possible path on bridging the gap between Cognitive Science and Computational Logic. We investigated findings from psychological experiments and modeled their results within one formal approach, the Weak Completion Semantics. Furthermore, we proposed a general evaluation system for conditionals, for which we suggest a specific evaluation strategy. Yet, the outcome cannot be seen as the ultimate solution but delivers a starting point for new open questions in both areas

Every normal logic program has a 2-valued semantics: theory, extensions, applications, implementations

Trabalho apresentado no âmbito do Doutoramento em Informática, como requisito parcial para obtenção do grau de Doutor em InformáticaAfter a very brief introduction to the general subject of Knowledge Representation and Reasoning with Logic Programs we analyse the syntactic structure of a logic program and how it can influence the semantics. We outline the important properties of a 2-valued semantics for Normal Logic Programs, proceed to define the new Minimal Hypotheses semantics with those properties and explore how it can be used to benefit some knowledge representation and reasoning mechanisms. The main original contributions of this work, whose connections will be detailed in the sequel, are: • The Layering for generic graphs which we then apply to NLPs yielding the Rule Layering and Atom Layering — a generalization of the stratification notion; • The Full shifting transformation of Disjunctive Logic Programs into (highly nonstratified)NLPs; • The Layer Support — a generalization of the classical notion of support; • The Brave Relevance and Brave Cautious Monotony properties of a 2-valued semantics; • The notions of Relevant Partial Knowledge Answer to a Query and Locally Consistent Relevant Partial Knowledge Answer to a Query; • The Layer-Decomposable Semantics family — the family of semantics that reflect the above mentioned Layerings; • The Approved Models argumentation approach to semantics; • The Minimal Hypotheses 2-valued semantics for NLP — a member of the Layer-Decomposable Semantics family rooted on a minimization of positive hypotheses assumption approach; • The definition and implementation of the Answer Completion mechanism in XSB Prolog — an essential component to ensure XSB’s WAM full compliance with the Well-Founded Semantics; • The definition of the Inspection Points mechanism for Abductive Logic Programs;• An implementation of the Inspection Points workings within the Abdual system [21] We recommend reading the chapters in this thesis in the sequence they appear. However, if the reader is not interested in all the subjects, or is more keen on some topics rather than others, we provide alternative reading paths as shown below. 1-2-3-4-5-6-7-8-9-12 Definition of the Layer-Decomposable Semantics family and the Minimal Hypotheses semantics (1 and 2 are optional) 3-6-7-8-10-11-12 All main contributions – assumes the reader is familiarized with logic programming topics 3-4-5-10-11-12 Focus on abductive reasoning and applications.FCT-MCTES (Fundação para a Ciência e Tecnologia do Ministério da Ciência,Tecnologia e Ensino Superior)- (no. SFRH/BD/28761/2006

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Disjunctive argumentation semantics (DAS) for reasoning over distributed uncertain knowledge.

by Benson, Ng Hin Kwong.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 111-117).Abstract also in Chinese.Chapter 1 --- Introduction --- p.9Chapter 1.1 --- Our approach --- p.11Chapter 1.2 --- Organization of the thesis --- p.12Chapter 2 --- Logic Programming --- p.13Chapter 2.1 --- Logic programming in Horn clauses --- p.14Chapter 2.1.1 --- Problem with incomplete information --- p.15Chapter 2.1.2 --- Problem with inconsistent information --- p.15Chapter 2.1.3 --- Problem with indefinite information --- p.16Chapter 2.2 --- Logic programming in non-Horn clauses --- p.16Chapter 2.2.1 --- Reasoning under incomplete information --- p.17Chapter 2.2.2 --- Reasoning under inconsistent information --- p.17Chapter 2.2.3 --- Reasoning under indefinite information --- p.20Chapter 2.3 --- "Coexistence of incomplete, inconsistent and indefinite information" --- p.21Chapter 2.4 --- Stable semantics --- p.22Chapter 2.5 --- Well-founded semantics --- p.23Chapter 2.6 --- Chapter summary --- p.25Chapter 3 --- Argumentation --- p.26Chapter 3.1 --- Toulmin's informal argumentation model --- p.27Chapter 3.2 --- Rescher's formal argumentation model --- p.28Chapter 3.3 --- Argumentation in AI research --- p.30Chapter 3.3.1 --- Poole's Logical Framework for Default Reasoning --- p.30Chapter 3.3.2 --- Inheritance Reasoning Framework of Touretzky et. al --- p.31Chapter 3.3.3 --- Pollock's Theory of Defeasible Reasoning --- p.32Chapter 3.3.4 --- Dung's Abstract Argumentation Framework --- p.33Chapter 3.3.5 --- Lin and Shoham's Argument System --- p.35Chapter 3.3.6 --- Vreeswijk's Abstract Argumentation --- p.35Chapter 3.3.7 --- Kowalski and Toni's Uniform Argumentation --- p.36Chapter 3.3.8 --- John Fox's Qualitative Argumentation --- p.37Chapter 3.3.9 --- Thomas Gordon's Pleading Games --- p.38Chapter 3.3.10 --- Chris Reed's Persuasive Dialogue --- p.39Chapter 3.3.11 --- Ronald Loui's Argument Game --- p.39Chapter 3.3.12 --- "Verheij's Reason-Based, Logics and CumulA" --- p.40Chapter 3.3.13 --- Prakken's Defeasible Argumentation --- p.40Chapter 3.3.14 --- Summary of existing frameworks --- p.41Chapter 3.4 --- Chapter summary --- p.42Chapter 4 --- Disjunctive Argumentation Semantics I --- p.46Chapter 4.1 --- Background --- p.47Chapter 4.2 --- Definition --- p.48Chapter 4.3 --- Conflicts within a KBS --- p.52Chapter 4.4 --- Conflicts between KBSs --- p.54Chapter 4.4.1 --- Credulous View --- p.56Chapter 4.4.2 --- Skeptical View --- p.57Chapter 4.4.3 --- Generalized Skeptical View --- p.58Chapter 4.5 --- Semantics --- p.60Chapter 4.6 --- Dialectical proof theory --- p.61Chapter 4.7 --- Relation to existing framework --- p.61Chapter 4.8 --- Issue on paraconsistency --- p.63Chapter 4.9 --- An illustrative example --- p.63Chapter 4.10 --- Chapter summary --- p.65Chapter 5 --- Disjunctive Argumentation Semantics II --- p.67Chapter 5.1 --- Background --- p.68Chapter 5.2 --- Definition --- p.70Chapter 5.2.1 --- Rules --- p.70Chapter 5.2.2 --- Splits --- p.71Chapter 5.3 --- Conflicts --- p.74Chapter 5.3.1 --- Undercut conflicts --- p.75Chapter 5.3.2 --- Rebuttal conflicts --- p.76Chapter 5.3.3 --- Thinning conflicts --- p.78Chapter 5.4 --- Semantics --- p.80Chapter 5.5 --- Relation to existing frameworks --- p.81Chapter 5.6 --- Issue on paraconsistency --- p.82Chapter 5.7 --- An illustrative example --- p.83Chapter 5.8 --- Chapter summary --- p.85Chapter 6 --- Evaluation --- p.86Chapter 6.1 --- Introduction --- p.86Chapter 6.2 --- Methodology --- p.87Chapter 6.3 --- DAS I --- p.88Chapter 6.3.1 --- Inoue's Benchmark problems --- p.88Chapter 6.3.2 --- Sherlock Holmes' problems --- p.96Chapter 6.4 --- DAS II --- p.100Chapter 6.4.1 --- Inoue's benchmark problems --- p.100Chapter 6.4.2 --- Sherlock Holmes' problem --- p.103Chapter 6.5 --- Analysis --- p.103Chapter 6.5.1 --- Possible extension --- p.104Chapter 6.6 --- Chapter summary --- p.106Chapter 7 --- Conclusion --- p.108Chapter 7.0.1 --- Possible extension of the present work --- p.109Bibliography --- p.117Chapter A --- First Oreder Logic (FOL) --- p.118Chapter B --- DAS-I Proof --- p.121Chapter B.1 --- Monotone proof --- p.121Chapter B.2 --- Soundness proof --- p.122Chapter B.3 --- Completeness proof --- p.123Chapter C --- Sherlock Holmes' Silver Blaze Excerpts --- p.125Chapter C.1 --- Double life --- p.125Chapter C.2 --- Poison stable boy --- p.12

Human reasoning and cognitive science

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain

Kiel Declarative Programming Days 2013

This report contains the papers presented at the Kiel Declarative Programming Days 2013, held in Kiel (Germany) during September 11-13, 2013. The Kiel Declarative Programming Days 2013 unified the following events: * 20th International Conference on Applications of Declarative Programming and Knowledge Management (INAP 2013) * 22nd International Workshop on Functional and (Constraint) Logic Programming (WFLP 2013) * 27th Workshop on Logic Programming (WLP 2013) All these events are centered around declarative programming, an advanced paradigm for the modeling and solving of complex problems. These specification and implementation methods attracted increasing attention over the last decades, e.g., in the domains of databases and natural language processing, for modeling and processing combinatorial problems, and for high-level programming of complex, in particular, knowledge-based systems