6,978 research outputs found
On Loop Formulas with Variables
Recently Ferraris, Lee and Lifschitz proposed a new definition of stable
models that does not refer to grounding, which applies to the syntax of
arbitrary first-order sentences. We show its relation to the idea of loop
formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop
formulas to disjunctive programs and to arbitrary first-order sentences. We
also extend the syntax of logic programs to allow explicit quantifiers, and
define its semantics as a subclass of the new language of stable models by
Ferraris et al. Such programs inherit from the general language the ability to
handle nonmonotonic reasoning under the stable model semantics even in the
absence of the unique name and the domain closure assumptions, while yielding
more succinct loop formulas than the general language due to the restricted
syntax. We also show certain syntactic conditions under which query answering
for an extended program can be reduced to entailment checking in first-order
logic, providing a way to apply first-order theorem provers to reasoning about
non-Herbrand stable models.Comment: 10 pages. In Proc. Eleventh International Conference on Principles of
Knowledge Representation and Reasoning (KR 2008), pages 444-453. arXiv admin
note: text overlap with arXiv:1401.389
CMODELS – SAT-based Disjunctive Answer Set Solver
Disjunctive logic programming under the stable model semantics [GL91] is a new methodology called answer set programming (ASP) for solving combinatorial search problems. This programming method uses answer set solvers, such as DLV [Lea05], GNT [Jea05], SMODELS [SS05], ASSAT [LZ02], CMODELS [Lie05a]. Systems DLV and GNT are more general as they work with the class of disjunctive logic programs, while other systems cover only normal programs. DLV is uniquely designed to find the answer sets for disjunctive logic programs. On the other hand, GNT first generates possible stable model candidates and then tests the candidate on the minimality using system SMODELS as an inference engine for both tasks. Systems CMODELS and ASSAT use SAT solvers as search engines. They are based on the relationship between the completion semantics [Cla78], loop formulas [LZ02] and answer set semantics for logic programs. Here we present the implementation of a SAT-based algorithm for finding answer sets for disjunctive logic programs within CMODELS. The work is based on the definition of completion for disjunctive programs [LL03] and the generalisation of loop formulas [LZ02] to the case of disjunctive programs [LL03].We propose the necessary modifications to the SAT based ASSAT algorithm [LZ02] as well as to the generate and test algorithmfrom [GLM04] in order to adapt them to the case of disjunctive programs. We implement the algorithms in CMODELS and demonstrate the experimental results
Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of
ICLP 2015
Recent advances in knowledge compilation introduced techniques to compile
\emph{positive} logic programs into propositional logic, essentially exploiting
the constructive nature of the least fixpoint computation. This approach has
several advantages over existing approaches: it maintains logical equivalence,
does not require (expensive) loop-breaking preprocessing or the introduction of
auxiliary variables, and significantly outperforms existing algorithms.
Unfortunately, this technique is limited to \emph{negation-free} programs. In
this paper, we show how to extend it to general logic programs under the
well-founded semantics.
We develop our work in approximation fixpoint theory, an algebraical
framework that unifies semantics of different logics. As such, our algebraical
results are also applicable to autoepistemic logic, default logic and abstract
dialectical frameworks
Propositional computability logic I
In the same sense as classical logic is a formal theory of truth, the
recently initiated approach called computability logic is a formal theory of
computability. It understands (interactive) computational problems as games
played by a machine against the environment, their computability as existence
of a machine that always wins the game, logical operators as operations on
computational problems, and validity of a logical formula as being a scheme of
"always computable" problems. The present contribution gives a detailed
exposition of a soundness and completeness proof for an axiomatization of one
of the most basic fragments of computability logic. The logical vocabulary of
this fragment contains operators for the so called parallel and choice
operations, and its atoms represent elementary problems, i.e. predicates in the
standard sense. This article is self-contained as it explains all relevant
concepts. While not technically necessary, however, familiarity with the
foundational paper "Introduction to computability logic" [Annals of Pure and
Applied Logic 123 (2003), pp.1-99] would greatly help the reader in
understanding the philosophy, underlying motivations, potential and utility of
computability logic, -- the context that determines the value of the present
results. Online introduction to the subject is available at
http://www.cis.upenn.edu/~giorgi/cl.html and
http://www.csc.villanova.edu/~japaridz/CL/gsoll.html .Comment: To appear in ACM Transactions on Computational Logi
Recycling Computed Answers in Rewrite Systems for Abduction
In rule-based systems, goal-oriented computations correspond naturally to the
possible ways that an observation may be explained. In some applications, we
need to compute explanations for a series of observations with the same domain.
The question whether previously computed answers can be recycled arises. A yes
answer could result in substantial savings of repeated computations. For
systems based on classic logic, the answer is YES. For nonmonotonic systems
however, one tends to believe that the answer should be NO, since recycling is
a form of adding information. In this paper, we show that computed answers can
always be recycled, in a nontrivial way, for the class of rewrite procedures
that we proposed earlier for logic programs with negation. We present some
experimental results on an encoding of the logistics domain.Comment: 20 pages. Full version of our IJCAI-03 pape
From truth to computability I
The recently initiated approach called computability logic is a formal theory
of interactive computation. See a comprehensive online source on the subject at
http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a
soundness and completeness proof for the deductive system CL3 which axiomatizes
the most basic first-order fragment of computability logic called the
finite-depth, elementary-base fragment. Among the potential application areas
for this result are the theory of interactive computation, constructive applied
theories, knowledgebase systems, systems for resource-bound planning and
action. This paper is self-contained as it reintroduces all relevant
definitions as well as main motivations.Comment: To appear in Theoretical Computer Scienc
Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs
We consider the problem of computing numerical invariants of programs, for
instance bounds on the values of numerical program variables. More
specifically, we study the problem of performing static analysis by abstract
interpretation using template linear constraint domains. Such invariants can be
obtained by Kleene iterations that are, in order to guarantee termination,
accelerated by widening operators. In many cases, however, applying this form
of extrapolation leads to invariants that are weaker than the strongest
inductive invariant that can be expressed within the abstract domain in use.
Another well-known source of imprecision of traditional abstract interpretation
techniques stems from their use of join operators at merge nodes in the control
flow graph. The mentioned weaknesses may prevent these methods from proving
safety properties. The technique we develop in this article addresses both of
these issues: contrary to Kleene iterations accelerated by widening operators,
it is guaranteed to yield the strongest inductive invariant that can be
expressed within the template linear constraint domain in use. It also eschews
join operators by distinguishing all paths of loop-free code segments. Formally
speaking, our technique computes the least fixpoint within a given template
linear constraint domain of a transition relation that is succinctly expressed
as an existentially quantified linear real arithmetic formula. In contrast to
previously published techniques that rely on quantifier elimination, our
algorithm is proved to have optimal complexity: we prove that the decision
problem associated with our fixpoint problem is in the second level of the
polynomial-time hierarchy.Comment: 35 pages, conference version published at ESOP 2011, this version is
a CoRR version of our submission to Logical Methods in Computer Scienc
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