RP-DeLP: a weighted defeasible argumentation framework based on a recursive semantics

In this paper we first define a recursive semantics for warranted formulas in a general defeasible argumentation framework by formalizing a notion of collective (non-binary) conflict among arguments. The recursive semantics for warranted formulas is based on the fact that if the argument is rejected, then all arguments built on it should also be rejected. The main characteristic of our recursive semantics is that an output (extension) of a knowledge base is a pair of sets of warranted and blocked formulas. Arguments for both warranted and blocked formulas are recursively based on warranted formulas but, while warranted formulas do not generate any collective conflict, blocked conclusions do. Formulas that are neither warranted nor blocked correspond to rejected formulas. Second we extend the general defeasible argumentation framework by attaching levels of preference to defeasible knowledge items and by providing a level-wise definition of warranted and blocked formulas. Third we formalize the warrant recursive semantics for the particular framework of Possibilistic Defeasible Logic Programming, we call this particular framework Recursive Possibilistic Defeasible Logic Programming (\mbox{RP-DeLP} for short), and we show its relevance in the scope of Political debates. An RP-DeLP program may have multiple outputs in case of circular definitions of conflicts among arguments. So, we tackle the problem of which output one should consider for an RP-DeLP program with multiple outputs. To this end we define the maximal ideal output of an RP-DeLP program as the set of conclusions which are ultimately warranted and we present an algorithm for computing them in polynomial space and with an upper bound on complexity equal to P^{NP}. Finally, we propose an efficient and scalable implementation of this algorithm that is based on implementing the two main queries of the system, looking for valid arguments and collective conflicts between arguments, using SAT encodings. We perform an experimental evaluation of our SAT based approach when solving test sets of instances with single and multiple preference levels for defeasible knowledge.The authors are very thankful to the anonymous reviewers for their helpful and constructive comments. This research was partially supported by the Spanish projects ARINF (TIN2009- 14704-C03-01), TASSAT (TIN2010-20967-C04-03), EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

A logic programming framework for possibilistic argumentation: formalization and logical properties

In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argument-based frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper presents Possibilistic Logic Programming (P-DeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on G¨odel fuzzy logic. One of the applications of P-DeLP is providing an intelligent agent with non-monotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two non-monotonic operators which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studie

A preliminary framework for reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PDLDA ontologies for short). PDLDA ontologies are composed of a terminology as well as an assertional box that allows to declare three kinds of assertional statements: an individual is a member of one concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Each axiom in the ontologies has a certainty degree as is usual in possibilistic logics. For reasoning with PDLDA ontologies, we interpret them in terms of a adaptation of Bodanza's Suppositional Argumentation System. Our framework allows to reason with modus ponens and constructive dilemmas. We use it for determining the membership of individuals to concepts when there is doubt to exactly which one of the concepts in the union the individual belongs. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.XVI Workshop Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

A preliminary framework for reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PDLDA ontologies for short). PDLDA ontologies are composed of a terminology as well as an assertional box that allows to declare three kinds of assertional statements: an individual is a member of one concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Each axiom in the ontologies has a certainty degree as is usual in possibilistic logics. For reasoning with PDLDA ontologies, we interpret them in terms of a adaptation of Bodanza's Suppositional Argumentation System. Our framework allows to reason with modus ponens and constructive dilemmas. We use it for determining the membership of individuals to concepts when there is doubt to exactly which one of the concepts in the union the individual belongs. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.XVI Workshop Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Formalisation and logical properties of the maximal ideal recursive semantics for weighted defeasible logic programming

Possibilistic defeasible logic programming (P-DeLP) is a logic programming framework which combines features from argumentation theory and logic programming, in which defeasible rules are attached with weights expressing their relative belief or preference strength. In P-DeLP,a conclusion succeeds if there exists an argument that entails the conclusion and this argument is found to be undefeated by a warrant procedure that systematically explores the universe of arguments in order to present an exhaustive synthesis of the relevant chains of pros and cons for the given conclusion. Recently, we have proposed a new warrant recursive semantics for P-DeLP, called Recursive P-DeLP (RP-DeLP for short), based on the claim that the acceptance of an argument should imply also the acceptance of all its sub-arguments which reflect the different premises on which the argument is based. This paper explores the relationship between the exhaustive dialectical analysis-based semantics of P-DeLP and the recursive-based semantics of RP-DeLP, and analyses a non-monotonic inference operator for RP-DeLP which models the expansion of a given program by adding new weighted facts associated with warranted conclusions. Given the recursive-based semantics of RP-DeLP, we have also implemented an argumentation framework for RP-DeLP that is able to compute not only the output of warranted and blocked conclusions, but also explain the reasons behind the status of each conclusion. We have developed this framework as a stand-alone application with a simple text-based input/output interface to be able to use it as part of other artificial intelligence systemsThis research was partially supported by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allows to reason with modus ponens and constructive dilemmas. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.Facultad de Informátic

Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allows to reason with modus ponens and constructive dilemmas. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.Facultad de Informátic

A Framework for Combining Defeasible Argumentation with Labeled Deduction

In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. Defeasible argumentation has proven to be a successful approach to formalizing commonsense reasoning, encompassing many other alternative formalisms for defeasible reasoning. Argument-based frameworks share some common notions (such as the concept of argument, defeater, etc.) along with a number of particular features which make it difficult to compare them with each other from a logical viewpoint. This paper introduces LDSar, a LDS for defeasible argumentation in which many important issues concerning defeasible argumentation are captured within a unified logical framework. We also discuss some logical properties and extensions that emerge from the proposed framework.Comment: 15 pages, presented at CMSRA Workshop 2003. Buenos Aires, Argentin

Towards a Practical Implementation of a Reasoner for Inconsistent Possibilistic Description Logic Programming Ontologies

This work reports on our e orts to implement a practical reasoner based on Dung-style argumentation semantics for potentially inconsistent possibilistic ontologies. Our Java-based implementation targets a subset of the description logic programming fragment that we codify in a Racer-like syntax suitably adapted for representing certainty degrees of both axioms and assertions. We introduce our approach with a running example, discuss implementation issues and present time complexity results.Sociedad Argentina de Informática e Investigación Operativa (SADIO