608 research outputs found
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 CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - BahĂa Blanca; ArgentinaFil: TohmĂ©, Fernando Abel. Universidad Nacional del Sur. Departamento de EconomĂa; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - BahĂa Blanca. Instituto de Investigaciones EconĂłmicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de EconomĂa. Instituto de Investigaciones EconĂłmicas 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
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
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
Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
In this work we study a rational extension 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
-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
Interdefinability of defeasible logic and logic programming under the well-founded semantics
We provide a method of translating theories of Nute's defeasible logic into
logic programs, and a corresponding translation in the opposite direction.
Under certain natural restrictions, the conclusions of defeasible theories
under the ambiguity propagating defeasible logic ADL correspond to those of the
well-founded semantics for normal logic programs, and so it turns out that the
two formalisms are closely related. Using the same translation of logic
programs into defeasible theories, the semantics for the ambiguity blocking
defeasible logic NDL can be seen as indirectly providing an ambiguity blocking
semantics for logic programs. We also provide antimonotone operators for both
ADL and NDL, each based on the Gelfond-Lifschitz (GL) operator for logic
programs. For defeasible theories without defeaters or priorities on rules, the
operator for ADL corresponds to the GL operator and so can be seen as partially
capturing the consequences according to ADL. Similarly, the operator for NDL
captures the consequences according to NDL, though in this case no restrictions
on theories apply. Both operators can be used to define stable model semantics
for defeasible theories.Comment: 36 pages; To appear in Theory and Practice of Logic Programming
(TPLP
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