On Extended Disjunctive Logic Programs

@inproceedings{Minker1993OnED,
  title={On Extended Disjunctive Logic Programs},
  author={Jack Minker and Carolina Ruiz},
  booktitle={ISMIS},
  year={1993}
}
This paper studies, in a comprehensive manner, different aspects of extended disjunctive logic programs, that is, programs whose clauses are of the form l1 ∨ ... ∨ l k ← lk+1, ..., l m , not lm+1,..., not l n , where l1,..., l n are literals (i.e. atoms and classically negated atoms), and not is the negation-by-default operator. The explicit use of classical negation suggests the introduction of a new truth value, namely, logical falsehood (in contrast to falsehood-by-default) in the semantics… 

Semantics for Disjunctive Logic Programs with Explicit and Default Negation

TLDR
This work studies the semantics of disjunctive programs that contain both explicit negation and negation-by-default, called extended disJunctive logic programs, and general techniques are described for extending model, fixpoint, and proof theoretic characterizations of an arbitrary semantics of normal disjunctions logic programs to cover the class of extended programs.

Negation and Minimality in Disjunctive Databases

Solving Practical Reasoning Poblems with Extended Disjunctive Logic Programming

TLDR
Besides being able to solve classical ATP problems in a monotonic reasoning mode, EDLP can as well treat commonsense reasoning problems by employing its intrinsic nonmonotonic inference capabilities based on stable generated models, which proves itself as a general-purpose AI reasoning system.

Using clausal deductive databases for defining semantics in disjunctive deductive databases

  • D. Seipel
  • Computer Science
    Annals of Mathematics and Artificial Intelligence
  • 2004
TLDR
This paper presents a transformation which maps a dd-database D into a cd- database Dcd that talks about the clauses of D, and presents a program transformation, which uses the idea of bringing sets of clauses to the argument level for hypothetical logic programs.

Computing Stable and Partial Stable Models of Extended Disjunctive Logic Programs

TLDR
This paper describes a procedure to compute the collection of all partial stable models of an extended disjunctive logic program whose set of 2-valued minimal models corresponds to the set of partialstable models of the original program.

Combining Closed World Assumptions with Stable Negation

We study the semantics of disjunctive logic programs that simultaneously contain multiple kinds of default negations. We introduce operators not G, not W, and not STB in the language of logic

Logic Programming and Knowledge Representation

TLDR
This paper considers extensions of the language of definite logic programs by classical (strong) negation, disjunction, and some modal operators and shows how each of the added features extends the representational power of thelanguage.

Paraconsistency and Beyond: A New Approach to Inconsistency Handling

  • S. Ghosh
  • Computer Science, Philosophy
    ISMIS
  • 1994
TLDR
This work proposes an inconsistency handling concept — explicit paraconsistency, formalized as ApproachC, which is close in spirit to ‘paraconsistent’ approaches known from the logicophilosophical literature on non-classical logics handling inconsistency.

Logic knowledge bases with two default rules

TLDR
A class of LKBS containing multiple forms of default negation in addition to explicit negation is described and the computational complexity of three main reasoning tasks for this semantics is calculated.

Solving the Steamroller, and Other Puzzles, with Extended Disjunctive Logic Programming

We show how to solve the classical ATP benchmark test problem Schu-bert's Steamroller, and other puzzles, in the nonclassical framework of extended disjunctive logic programming (EDLP) where neither

References

SHOWING 1-10 OF 41 REFERENCES

On Logic Program Semantics with Two Kinds of Negation

TLDR
The goal of this paper is to contrast a variety of these semantics in what concerns their use and meaning of :-negation, and its relation to classical negation and to the default negation of normal programs, here denoted by not.

Unfounded sets and well-founded semantics for general logic programs

TLDR
It is shown that a program has a unique stable model if it has a well-founded model, in which case they are the same, and the converse is not true.

Issues in knowledge representation: semantics and knowledge combination

TLDR
This thesis introduces the concept of "classes" to be able to characterize the class of all theories when they are represented as normal logic programs, default theories, auto-epistemic theories and non-monotonic modal theories, and presents a uniform framework for iterated fixpoint semantics of logic programs.

Embedding Negation as Failure into a Model Generation Theorem Prover

TLDR
An implementation which computes answer sets of every class of (function-free) logic programs and deductive databases containing both negation as failure and classical negation is given.

Foundations of disjunctive logic programming

TLDR
This paper discusses first-order theory - syntax first order theory - semantics logic programs - syntax Logic programs - semantics - models and interpretations substitutions and unifiers fixpoint theory, a comparison of definite and disjunctive logic programs and normal logic programs.

Computing Intersection of Autoepistemic Expansions

TLDR
This paper describes a method that assigns to a modal theory I a propositional theory PI and to amodal-free formula φ another formulaπ in such a manner that φ is in the intersection of all expansions of I if and only if PI ⊢ φ .

The Semantics of Predicate Logic as a Programming Language

TLDR
In this paper the operational and fixpoint semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated, and it is concluded that operational semantics is a part ofProof theory and that fixpoint semantic is a special case of model-theoretic semantics.

Computing intersection of autoepis-temic expansions

TLDR
This paper describes a method that assigns to a modal theory I a propositional theory PI and to amodal-free formula φ another formulaπ in such a manner that φ is in the intersection of all expansions of I if and only if PI ⊢ φ .