Hypothetical reasoning and definitional reflection in logic programming

AbstractLogic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of alternative semantics, with Kripke–Kleene semantics, the well-founded semantics, the stable model semantics, and the answer-set semantics standing out as the most successful. We show that all aforementioned semantics are particular cases of a generic semantics, in a framework where classical negation is the unique form of negation and where the literals in the bodies of the rules can be ‘marked’ to indicate that they can be the targets of hypotheses. A particular semantics then amounts to choosing a particular marking scheme and choosing a particular set of hypotheses. When a literal belongs to the chosen set of hypotheses, all marked occurrences of that literal in the body of a rule are assumed to be true, whereas the occurrences of that literal that have not been marked in the body of the rule are to be derived in order to contribute to the firing of the rule. Hence the notion of hypothetical reasoning that is presented in this framework is not based on making global assumptions, but more subtly on making local, contextual assumptions, taking effect as indicated by the chosen marking scheme on the basis of the chosen set of hypotheses. Our approach offers a unified view on the various semantics proposed in logic programming, classical in that only classical negation is used, and links the semantics of logic programs to mechanisms that endow rule-based systems with the power to harness hypothetical reasoning.

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A modal extension of logic programming: modularity, beliefs and hypothetical reasoning

Journal of Logic and Computation ◽

10.1093/logcom/8.5.597 ◽

1998 ◽

Vol 8 (5) ◽

pp. 597-635 ◽

Cited By ~ 15

Author(s):

M Baldoni

Keyword(s):

Logic Programming ◽

Hypothetical Reasoning ◽

Modal Extension

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Hypothetical reasoning in logic programming: a semantic approach

Information Processing Letters ◽

10.1016/0020-0190(90)90040-5 ◽

1990 ◽

Vol 36 (6) ◽

pp. 285-291 ◽

Cited By ~ 2

Author(s):

Antonio Brogi ◽

Evelina Lamma ◽

Paula Mello

Keyword(s):

Logic Programming ◽

Hypothetical Reasoning ◽

Semantic Approach

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CONCURRENT ABDUCTIVE LOGIC PROGRAMMING IN PANDORA

International Journal of Artificial Intelligence Tools ◽

10.1142/s021821300100057x ◽

2001 ◽

Vol 10 (03) ◽

pp. 387-406

Author(s):

REEM BAHGAT ◽

OSAMA MOSTAFA ◽

GEORGE A. PAPADOPOULOS

Keyword(s):

Logic Programming ◽

Logic Program ◽

The Other ◽

Logic Programs ◽

Hypothetical Reasoning ◽

Concurrent Logic Programming ◽

Programming Technique ◽

Abductive Logic ◽

Abductive Logic Programming ◽

Distributed Execution

The extension of logic programming with abduction (ALP) allows a form of hypothetical reasoning. The advantages of abduction lie in the ability to reason with incomplete information and the enhancement of the declarative representation of problems. On the other hand, concurrent logic programming is a framework which explores AND-parallelism and/or OR-parallelism in logic programs in order to efficiently execute them on multi-processor / distributed machines. The aim of our work is to study a way to model abduction within the framework of concurrent logic programming, thus taking advantage of the latter's potential for parallel and/or distributed execution. In particular, we describe Abductive Pandora, a syntactic sugar on top of the concurrent logic programming language Pandora, which provides the user with an abductive behavior for a concurrent logic program. Abductive Pandora programs are then transformed into Pandora programs which support the concurrent abductive behavior through a simple programming technique while at the same time taking advantage of the underlying Pandora machine infrastructure.

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