Defeasible Reasoning via Datalog¬

2021 ◽  
pp. 1-43
Author(s):  
MICHAEL J. MAHER
Keyword(s):  
Structural Properties ◽  
Efficient Implementation ◽  
Defeasible Reasoning ◽  
Logic Programs ◽  
Defeasible Logic

Abstract We address the problem of compiling defeasible theories to Datalog¬ programs. We prove the correctness of this compilation, for the defeasible logic DL(∂||), but the techniques we use apply to many other defeasible logics. Structural properties of DL(∂||) are identified that support efficient implementation and/or approximation of the conclusions of defeasible theories in the logic, compared with other defeasible logics. We also use previously well-studied structural properties of logic programs to adapt to incomplete Datalog¬ implementations.

scholarly journals Interdefinability of defeasible logic and logic programming under the well-founded semantics

2011 ◽  
Vol 13 (1) ◽  
pp. 107-142 ◽  
Author(s):  
FREDERICK MAIER
Keyword(s):  
Logic Programming ◽  
Opposite Direction ◽  
Stable Model ◽  
Logic Programs ◽  
Defeasible Logic ◽  
Normal Logic

AbstractWe 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.

scholarly journals Annotated defeasible logic

2017 ◽  
Vol 17 (5-6) ◽  
pp. 819-836 ◽  
Author(s):  
GUIDO GOVERNATORI ◽  
MICHAEL J. MAHER
Keyword(s):  
Defeasible Reasoning ◽  
Multiple Forms ◽  
Linguistic Features ◽  
Defeasible Logic

AbstractDefeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only combine in trivial ways. This limits their usefulness in contexts where different intuitions are at play in different aspects of a problem. In particular, in some legal settings, different actors have different burdens of proof, which might be expressed as reasoning in different defeasible logics. In this paper, we introduce annotated defeasible logic as a flexible formalism permitting multiple forms of defeasibility, and establish some properties of the formalism.

scholarly journals Argumentation and Defeasible Reasoning in the Law

J ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 897-914
Author(s):  
Marco Billi ◽  
Roberta Calegari ◽  
Giuseppe Contissa ◽  
Francesca Lagioia ◽  
Giuseppe Pisano ◽  
...  
Keyword(s):  
Knowledge Representation ◽  
Real World ◽  
Answer Set Programming ◽  
Defeasible Reasoning ◽  
Logical Model ◽  
Defeasible Logic ◽  
The Law ◽  
Legal Domain ◽  
Answer Set

Different formalisms for defeasible reasoning have been used to represent knowledge and reason in the legal field. In this work, we provide an overview of the following logic-based approaches to defeasible reasoning: defeasible logic, Answer Set Programming, ABA+, ASPIC+, and DeLP. We compare features of these approaches under three perspectives: the logical model (knowledge representation), the method (computational mechanisms), and the technology (available software resources). On top of that, two real examples in the legal domain are designed and implemented in ASPIC+ to showcase the benefit of an argumentation approach in real-world domains. The CrossJustice and Interlex projects are taken as a testbed, and experiments are conducted with the Arg2P technology.

scholarly journals Tabling with Sound Answer Subsumption

2016 ◽  
Vol 16 (5-6) ◽  
pp. 933-949 ◽  
Author(s):  
ALEXANDER VANDENBROUCKE ◽  
MACIEJ PIRÓG ◽  
BENOIT DESOUTER ◽  
TOM SCHRIJVERS
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Efficient Implementation ◽  
Logic Programs ◽  
Formal Framework ◽  
Fixed Point Semantics ◽  
Do So

AbstractTabling is a powerful resolution mechanism for logic programs that captures their least fixed point semantics more faithfully than plain Prolog. In many tabling applications, we are not interested in the set of all answers to a goal, but only require an aggregation of those answers. Several works have studied efficient techniques, such as lattice-based answer subsumption and mode-directed tabling, to do so for various forms of aggregation.While much attention has been paid to expressivity and efficient implementation of the different approaches, soundness has not been considered. This paper shows that the different implementations indeed fail to produce least fixed points for some programs. As a remedy, we provide a formal framework that generalises the existing approaches and we establish a soundness criterion that explains for which programs the approach is sound.

scholarly journals Conflict Resolution in Structured Argumentation

10.29007/brgz ◽  
2018 ◽  
Author(s):  
Martin Baláž ◽  
Jozef Frtús ◽  
Martin Homola
Keyword(s):  
Conflict Resolution ◽  
Logic Programming ◽  
Inference Rules ◽  
Logic Programs ◽  
Defeasible Logic ◽  
Structured Argumentation ◽  
Conflict Resolutions

While several interesting argumentation-based semantics fordefeasible logic programs have been proposed, to our bestknowledge, none of these approaches is able to fully handle theclosure under strict rules in a sufficient manner: they are eithernot closed, or they use workarounds such as transposition of ruleswhich violates the desired directionality of logic programmingrules.We propose a novel argumentation-based semantics, in which thestatus of arguments is determined by attacks between newlyintroduced conflict resolutions instead of attacks betweenarguments. We show that the semantics is closed w.r.t. strictrules and respects the directionality of inference rules, as wellas other desired properties previously published in theliterature.

scholarly journals Visual Development of Defeasible Logic Rules for the Semantic Web

2011 ◽  
pp. 273-301
Author(s):  
Efstratios Kontopoulos ◽  
Nick Bassiliades
Keyword(s):  
Semantic Web ◽  
Graphical Representation ◽  
Directed Graphs ◽  
Visual Development ◽  
Defeasible Reasoning ◽  
End User ◽  
Defeasible Logic ◽  
Suitable Tool

This chapter is concerned with the visualization of defeasible logic rules in the Semantic Web domain. Logic plays an important role in the development of the Semantic Web and defeasible reasoning seems to be a very suitable tool. However, it is too complex for an end-user, who often needs graphical trace and explanation mechanisms for the derived conclusions. Directed graphs can assist in this affair, by offering the notion of direction that appears to be extremely applicable for the representation of rule attacks and superiorities in defeasible reasoning. Their applicability, however, is balanced by the fact that it is difficult to associate data of a variety of types with the nodes and the connections between the nodes in the graph. In this chapter we try to utilize digraphs in the graphical representation of defeasible rules, by exploiting the expressiveness and comprehensibility they offer, but also trying to leverage their major disadvantages. Finally, the chapter briefly presents a tool that implements this representation methodology.

scholarly journals Dynamics of knowledge in DeLP through Argument Theory Change

2012 ◽  
Vol 13 (6) ◽  
pp. 893-957 ◽  
Author(s):  
MARTÍN O. MOGUILLANSKY ◽  
NICOLÁS D. ROTSTEIN ◽  
MARCELO A. FALAPPA ◽  
ALEJANDRO J. GARCÍA ◽  
GUILLERMO R. SIMARI
Keyword(s):  
Theory Change ◽  
Knowledge Bases ◽  
Minimal Change ◽  
Logic Programs ◽  
Rule Based ◽  
Defeasible Logic ◽  
Abstract Argumentation ◽  
Revision Operations ◽  
Argumentation Systems ◽  
Article Abstract

AbstractThis article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to reason over potentially inconsistent de.l.p.s. Argument Theory Change (ATC) studies certain aspects of belief revision in order to make them suitable for abstract argumentation systems. In this article, abstract arguments are rendered concrete by using the particular rule-based defeasible logic adopted by DeLP. The objective of our proposal is to define prioritized argument revision operators à la ATC for de.l.p.s, in such a way that the newly inserted argument ends up undefeated after the revision, thus warranting its conclusion. In order to ensure this warrant, the de.l.p. has to be changed in concordance with a minimal change principle. To this end, we discuss different minimal change criteria that could be adopted. Finally, an algorithm is presented, implementing the argument revision operations.

A declarative extension of horn clauses, and its significance for datalog and its applications

2013 ◽  
Vol 13 (4-5) ◽  
pp. 609-623 ◽  
Author(s):  
MIRJANA MAZURAN ◽  
EDOARDO SERRA ◽  
CARLO ZANIOLO
Keyword(s):  
Efficient Implementation ◽  
Logic Programs ◽  
Horn Clauses ◽  
Magic Sets ◽  
Fixpoint Semantics ◽  
Monotonic Extension ◽  
Stable Models

AbstractFS-rules provide a powerful monotonic extension for Horn clauses that supports monotonic aggregates in recursion by reasoning on the multiplicity of occurrences satisfying existential goals. The least fixpoint semantics, and its equivalent least model semantics, hold for logic programs with FS-rules; moreover, generalized notions of stratification and stable models are easily derived when negated goals are allowed. Finally, the generalization of techniques such as seminaive fixpoint and magic sets, make possible the efficient implementation of DatalogFS, i.e., Datalog with rules with Frequency Support (FS-rules) and stratified negation. A large number of applications that could not be supported efficiently, or could not be expressed at all in stratified Datalog can now be easily expressed and efficiently supported in DatalogFS and a powerful DatalogFS system is now being developed at UCLA.

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