74,377 research outputs found
On completeness of logic programs
Program correctness (in imperative and functional programming) splits in
logic programming into correctness and completeness. Completeness means that a
program produces all the answers required by its specification. Little work has
been devoted to reasoning about completeness. This paper presents a few
sufficient conditions for completeness of definite programs. We also study
preserving completeness under some cases of pruning of SLD-trees (e.g. due to
using the cut).
We treat logic programming as a declarative paradigm, abstracting from any
operational semantics as far as possible. We argue that the proposed methods
are simple enough to be applied, possibly at an informal level, in practical
Prolog programming. We point out importance of approximate specifications.Comment: 20 page
Proving Correctness and Completeness of Normal Programs - a Declarative Approach
We advocate a declarative approach to proving properties of logic programs.
Total correctness can be separated into correctness, completeness and clean
termination; the latter includes non-floundering. Only clean termination
depends on the operational semantics, in particular on the selection rule. We
show how to deal with correctness and completeness in a declarative way,
treating programs only from the logical point of view. Specifications used in
this approach are interpretations (or theories). We point out that
specifications for correctness may differ from those for completeness, as
usually there are answers which are neither considered erroneous nor required
to be computed.
We present proof methods for correctness and completeness for definite
programs and generalize them to normal programs. For normal programs we use the
3-valued completion semantics; this is a standard semantics corresponding to
negation as finite failure. The proof methods employ solely the classical
2-valued logic. We use a 2-valued characterization of the 3-valued completion
semantics which may be of separate interest. The presented methods are compared
with an approach based on operational semantics. We also employ the ideas of
this work to generalize a known method of proving termination of normal
programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP). 44
page
Memoization for Unary Logic Programming: Characterizing PTIME
We give a characterization of deterministic polynomial time computation based
on an algebraic structure called the resolution semiring, whose elements can be
understood as logic programs or sets of rewriting rules over first-order terms.
More precisely, we study the restriction of this framework to terms (and logic
programs, rewriting rules) using only unary symbols. We prove it is complete
for polynomial time computation, using an encoding of pushdown automata. We
then introduce an algebraic counterpart of the memoization technique in order
to show its PTIME soundness. We finally relate our approach and complexity
results to complexity of logic programming. As an application of our
techniques, we show a PTIME-completeness result for a class of logic
programming queries which use only unary function symbols.Comment: Soumis {\`a} LICS 201
Measuring Coverage of Prolog Programs Using Mutation Testing
Testing is an important aspect in professional software development, both to
avoid and identify bugs as well as to increase maintainability. However,
increasing the number of tests beyond a reasonable amount hinders development
progress. To decide on the completeness of a test suite, many approaches to
assert test coverage have been suggested. Yet, frameworks for logic programs
remain scarce.
In this paper, we introduce a framework for Prolog programs measuring test
coverage using mutations. We elaborate the main ideas of mutation testing and
transfer them to logic programs. To do so, we discuss the usefulness of
different mutations in the context of Prolog and empirically evaluate them in a
new mutation testing framework on different examples.Comment: 16 pages, Accepted for presentation in WFLP 201
An algebraic generalization of Kripke structures
The Kripke semantics of classical propositional normal modal logic is made
algebraic via an embedding of Kripke structures into the larger class of
pointed stably supported quantales. This algebraic semantics subsumes the
traditional algebraic semantics based on lattices with unary operators, and it
suggests natural interpretations of modal logic, of possible interest in the
applications, in structures that arise in geometry and analysis, such as
foliated manifolds and operator algebras, via topological groupoids and inverse
semigroups. We study completeness properties of the quantale based semantics
for the systems K, T, K4, S4, and S5, in particular obtaining an axiomatization
for S5 which does not use negation or the modal necessity operator. As
additional examples we describe intuitionistic propositional modal logic, the
logic of programs PDL, and the ramified temporal logic CTL.Comment: 39 page
Hybrid Rules with Well-Founded Semantics
A general framework is proposed for integration of rules and external first
order theories. It is based on the well-founded semantics of normal logic
programs and inspired by ideas of Constraint Logic Programming (CLP) and
constructive negation for logic programs. Hybrid rules are normal clauses
extended with constraints in the bodies; constraints are certain formulae in
the language of the external theory. A hybrid program is a pair of a set of
hybrid rules and an external theory. Instances of the framework are obtained by
specifying the class of external theories, and the class of constraints. An
example instance is integration of (non-disjunctive) Datalog with ontologies
formalized as description logics.
The paper defines a declarative semantics of hybrid programs and a
goal-driven formal operational semantics. The latter can be seen as a
generalization of SLS-resolution. It provides a basis for hybrid
implementations combining Prolog with constraint solvers. Soundness of the
operational semantics is proven. Sufficient conditions for decidability of the
declarative semantics, and for completeness of the operational semantics are
given
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