200 research outputs found
Tight Logic Programs
This note is about the relationship between two theories of negation as
failure -- one based on program completion, the other based on stable models,
or answer sets. Francois Fages showed that if a logic program satisfies a
certain syntactic condition, which is now called ``tightness,'' then its stable
models can be characterized as the models of its completion. We extend the
definition of tightness and Fages' theorem to programs with nested expressions
in the bodies of rules, and study tight logic programs containing the
definition of the transitive closure of a predicate.Comment: To appear in Special Issue of the Theory and Practice of Logic
Programming Journal on Answer Set Programming, 200
Representing First-Order Causal Theories by Logic Programs
Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner,
became a basis for the semantics of several expressive action languages.
McCain's embedding of definite propositional causal theories into logic
programming paved the way to the use of answer set solvers for answering
queries about actions described in such languages. In this paper we extend this
embedding to nondefinite theories and to first-order causal logic.Comment: 29 pages. To appear in Theory and Practice of Logic Programming
(TPLP); Theory and Practice of Logic Programming, May, 201
Intelligent Instantiation and Supersafe Rules
In the input languages of most answer set solvers, a rule with variables has, conceptually, infinitely many instances. The primary role of the process of intelligent instillation is to identify a finite set of ground instances of rules of the given program that are "essential" for generating its stable models. This process can be launched only when all rules of the program are safe. If a program contains arithmetic operations or comparisons then its rules are expected to satisfy conditions that are even stronger than safety. This paper is an attempt to make the idea of an essential instance and the need for "supersafety" in the process of intelligent instantiation mathematically
precise
Temporal Phylogenetic Networks and Logic Programming
The concept of a temporal phylogenetic network is a mathematical model of
evolution of a family of natural languages. It takes into account the fact that
languages can trade their characteristics with each other when linguistic
communities are in contact, and also that a contact is only possible when the
languages are spoken at the same time. We show how computational methods of
answer set programming and constraint logic programming can be used to generate
plausible conjectures about contacts between prehistoric linguistic
communities, and illustrate our approach by applying it to the evolutionary
history of Indo-European languages.
To appear in Theory and Practice of Logic Programming (TPLP)
On the Semantics of Gringo
Input languages of answer set solvers are based on the mathematically simple
concept of a stable model. But many useful constructs available in these
languages, including local variables, conditional literals, and aggregates,
cannot be easily explained in terms of stable models in the sense of the
original definition of this concept and its straightforward generalizations.
Manuals written by designers of answer set solvers usually explain such
constructs using examples and informal comments that appeal to the user's
intuition, without references to any precise semantics. We propose to approach
the problem of defining the semantics of gringo programs by translating them
into the language of infinitary propositional formulas. This semantics allows
us to study equivalent transformations of gringo programs using natural
deduction in infinitary propositional logic.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms
(ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke
On Equivalence of Infinitary Formulas under the Stable Model Semantics
Propositional formulas that are equivalent in intuitionistic logic, or in its
extension known as the logic of here-and-there, have the same stable models. We
extend this theorem to propositional formulas with infinitely long conjunctions
and disjunctions and show how to apply this generalization to proving
properties of aggregates in answer set programming. To appear in Theory and
Practice of Logic Programming (TPLP)
Fages' Theorem and Answer Set Programming
We generalize a theorem by Francois Fages that describes the relationship
between the completion semantics and the answer set semantics for logic
programs with negation as failure. The study of this relationship is important
in connection with the emergence of answer set programming. Whenever the two
semantics are equivalent, answer sets can be computed by a satisfiability
solver, and the use of answer set solvers such as smodels and dlv is
unnecessary. A logic programming representation of the blocks world due to
Ilkka Niemelae is discussed as an example
On Program Completion, with an Application to the Sum and Product Puzzle
This paper describes a generalization of Clark's completion that is
applicable to logic programs containing arithmetic operations and produces
syntactically simple, natural looking formulas. If a set of first-order axioms
is equivalent to the completion of a program then we may be able to find
standard models of these axioms by running an answer set solver. As an example,
we apply this "reverse completion" procedure to the Sum and Product Puzzle.Comment: Submitted to the 2023 International Conference on Logic Programmin
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