Embedding Defeasible Logic into Logic Programming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.Comment: To appear in Theory and Practice of Logic Programmin

Local logics, non-monotonicity and defeasible argumentation

In this paper we present an embedding of abstract argumentation systems into the framework of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of argument systems leads to a corresponding ordering of background conditions. The relations among extensions becomes a relation among partial orderings of background conditions. This introduces a conceptual innovation in Barwise and Seligman’s representation of commonsense reasoning.Fil: Bodanza, Gustavo Adrian. Universidad Nacional del Sur. Departamento de Humanidades; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Universidad Nacional del Sur. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure

Adaptive logic characterizations of input/output logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions

Disjunctive Logic Programs with Inheritance

The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language providing a natural representation of default reasoning with exceptions. A declarative model-theoretic semantics of DLP< is provided, which is shown to generalize the Answer Set Semantics of disjunctive logic programs. The knowledge modeling features of the language are illustrated by encoding classical nonmonotonic problems in DLP<. The complexity of DLP< is analyzed, proving that inheritance does not cause any computational overhead, as reasoning in DLP< has exactly the same complexity as reasoning in disjunctive logic programming. This is confirmed by the existence of an efficient translation from DLP< to plain disjunctive logic programming. Using this translation, an advanced KR system supporting the DLP< language has been implemented on top of the DLV system and has subsequently been integrated into DLV.Comment: 28 pages; will be published in Theory and Practice of Logic Programmin

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica