1,219 research outputs found
One More Decidable Class of Finitely Ground Programs
When a logic program is processed by an answer set solver, the first task is to generate its instantiation. In a recent paper, Calimeri et el. made the idea of efficient instantiation precise for the case of disjunctive programs with function symbols, and introduced the class of “finitely ground” programs that can be efficiently instantiated. Since that class is undecidable, it is important to find its large decidable subsets. In this paper, we introduce such a subset—the class of argumentrestricted programs. It includes, in particular, all finite domain programs, ω-restricted programs, and λ-restricted programs
One More Decidable Class of Finitely Ground Programs
Abstract. When a logic program is processed by an answer set solver, the first task is to generate its instantiation. In a recent paper, Calimeri et el. made the idea of efficient instantiation precise for the case of disjunctive programs with function symbols, and introduced the class of “finitely ground ” programs that can be efficiently instantiated. Since that class is undecidable, it is important to find its large decidable subsets. In this paper, we introduce such a subset—the class of argument-restricted programs. It includes, in particular, all finite domain programs, ω-restricted programs, and λ-restricted programs.
Disjunctive ASP with Functions: Decidable Queries and Effective Computation
Querying over disjunctive ASP with functions is a highly undecidable task in
general. In this paper we focus on disjunctive logic programs with stratified
negation and functions under the stable model semantics (ASP^{fs}). We show
that query answering in this setting is decidable, if the query is finitely
recursive (ASP^{fs}_{fr}). Our proof yields also an effective method for query
evaluation. It is done by extending the magic set technique to ASP^{fs}_{fr}.
We show that the magic-set rewritten program is query equivalent to the
original one (under both brave and cautious reasoning). Moreover, we prove that
the rewritten program is also finitely ground, implying that it is decidable.
Importantly, finitely ground programs are evaluable using existing ASP solvers,
making the class of ASP^{fs}_{fr} queries usable in practice.Comment: 16 pages, 1 figur
A decidable subclass of finitary programs
Answer set programming - the most popular problem solving paradigm based on
logic programs - has been recently extended to support uninterpreted function
symbols. All of these approaches have some limitation. In this paper we propose
a class of programs called FP2 that enjoys a different trade-off between
expressiveness and complexity. FP2 programs enjoy the following unique
combination of properties: (i) the ability of expressing predicates with
infinite extensions; (ii) full support for predicates with arbitrary arity;
(iii) decidability of FP2 membership checking; (iv) decidability of skeptical
and credulous stable model reasoning for call-safe queries. Odd cycles are
supported by composing FP2 programs with argument restricted programs
On finitely recursive programs
Disjunctive finitary programs are a class of logic programs admitting
function symbols and hence infinite domains. They have very good computational
properties, for example ground queries are decidable while in the general case
the stable model semantics is highly undecidable. In this paper we prove that a
larger class of programs, called finitely recursive programs, preserves most of
the good properties of finitary programs under the stable model semantics,
namely: (i) finitely recursive programs enjoy a compactness property; (ii)
inconsistency checking and skeptical reasoning are semidecidable; (iii)
skeptical resolution is complete for normal finitely recursive programs.
Moreover, we show how to check inconsistency and answer skeptical queries using
finite subsets of the ground program instantiation. We achieve this by
extending the splitting sequence theorem by Lifschitz and Turner: We prove that
if the input program P is finitely recursive, then the partial stable models
determined by any smooth splitting omega-sequence converge to a stable model of
P.Comment: 26 pages, Preliminary version in Proc. of ICLP 2007, Best paper awar
Progression and Verification of Situation Calculus Agents with Bounded Beliefs
We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories. © 2015 The Author(s
Infinite time decidable equivalence relation theory
We introduce an analog of the theory of Borel equivalence relations in which
we study equivalence relations that are decidable by an infinite time Turing
machine. The Borel reductions are replaced by the more general class of
infinite time computable functions. Many basic aspects of the classical theory
remain intact, with the added bonus that it becomes sensible to study some
special equivalence relations whose complexity is beyond Borel or even
analytic. We also introduce an infinite time generalization of the countable
Borel equivalence relations, a key subclass of the Borel equivalence relations,
and again show that several key properties carry over to the larger class.
Lastly, we collect together several results from the literature regarding Borel
reducibility which apply also to absolutely Delta_1^2 reductions, and hence to
the infinite time computable reductions.Comment: 30 pages, 3 figure
- …