Logic programming with satisfiability

Eprint Arxiv Cs 0003026, 2000

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query containing the variables of the constraint satisfaction problem. On the other hand there are approaches based on stable model semantics, abduction, and first-order logic model generation that compute solutions as models of some theory. This paper compares these different approaches from point of view of knowledge representation (how declarative are the programs) and from point of view of performance (how good are they at solving typical problems).

Lecture Notes in Artificial Intelligence, 2000

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the variables of the constraint satisfaction problem. On the other hand there are systems based on stable model semantics, abductive systems, and first order logic model generators which compute solutions as models of some theory. This paper compares these different approaches from the point of view of knowledge representation (how declarative are the programs) and from the point of view of performance (how good are they at solving typical problems).

2002

The availability of decision procedures for combinations of boolean and linear mathematical propositions opens the ability to solve problems arising from real-world domains such as verification of timed systems and planning with resources. In this paper we present a general and efficient approach to the problem, based on two main ingredients. The first is a DPLL-based SAT procedure, for dealing efficiently with the propositional component of the problem. The second is a tight integration, within the DPLL architecture, of a set of mathematical deciders for theories of increasing expressive power. A preliminary experimental evaluation shows the potential of the approach.

Theory and Practice of Logic Programming, 2010

This paper presents a logic language for expressing NP search and optimization problems. Specifically, first a language obtained by extending (positive) DATALOG with intuitive and efficient constructs (namely, stratified negation, constraints and exclusive disjunction) is introduced. Next, a further restricted language only using a restricted form of disjunction to define (non-deterministically) subsets (or partitions) of relations is investigated. This language, called NP Datalog , captures the power of DATALOG ¬ in expressing search and optimization problems. A system prototype implementing NP Datalog is presented. The system translates NP Datalog queries into OPL programs which are executed by the ILOG OPL Development Studio. Our proposal combines easy formulation of problems, expressed by means of a declarative logic language, with the efficiency of the ILOG System. Several experiments show the effectiveness of this approach.

Current and Future Trends

It is well known that NP search and optimization problems can be formulated as DATALOG¬ (datalog with unstratified negation; Abiteboul, Hull, & Vianu, 1994) queries under nondeterministic stable-model semantics so that each stable model corresponds to a possible solution (Gelfond & Lifschitz, 1988; Greco & Saccà, 1997; Kolaitis & Thakur, 1994). Although the use of (declarative) logic languages facilitates the process of writing complex applications, the use of unstratified negation allows programs to be written that in some cases are neither intuitive nor efficiently valuable. This article presents the logic language NP Datalog, a restricted version of DATALOG¬ that admits only controlled forms of negation, such as stratified negation, exclusive disjunction, and constraints. NP Datalog has the same expressive power as DATALOG¬, enables a simpler and intuitive formulation for search and optimization problems, and can be easily translated into other formalisms. The example below shows...

Lecture Notes in Computer Science, 1993

The purpose of this work is to define a theorem prover that retains the procedural aspects of logic programing. The proof system we propose (SLWV 1 resolution) is defined for a set of clauses in the implicational form (keeping to the form of logic programs), not requiring contrapositives, and has an execution method that respects the execution order of literals in a clause, preserving the procedural flavor of logic programming. SLWV resolution can be seen as a combination of SL-resolution [Chan73] and case-analysis, that admits a form of linear derivation. We prove its soundness and completeness, give it an operational semantics by defining a standard derivation, and produce an implementation. Our work can be seen as an extension to logic programs that goes beyond normal programs, as defined in [Lloy87], and thus beyond(positive) definite clause programming, by allowing also definite negative heads. Thus we admit program clauses with both positive and (classically) negated atoms conjoined in the body, and at most one literal as its head (clauses with disjunctions of literals in the head are transformed into a single clause of that form). As this approach does not require alternative clause contrapositives, it provides for better control over the search space. We provide a method of execution keeping to the implicational clausal form of program statements typical of Prolog (without the use of clause contrapositives), adding an increased expressiveness, but at a tolerable computational cost for regular Prolog programs. The implementation relies on the source program being preprocessed into directly executable Prolog. Since preprocessing only involves the addition of three additional variables to each predicate definition while keeping the overall program structure untouched, a directly recognizable execution pattern that mimics Prolog is obtained: this can be useful in debugging.

2005

This year marks the 40th anniversary of Alan Robinson's seminal paper on "A Machine-Oriented Logic Based on the Resolution Principle" that forms a basis for automated deduction and in particular logic programming, that started some three decades ago with the work of Robert Kowalski and Alain Colmerauer. The workshop on (constraint) logic programming is the annual meeting of the Society of Logic Programming (GLP e.V.) and brings together researchers interested in logic programming, constraint programming, and related areas like databases and artificial intelligence. Previous workshops have been held in Germany, Austria, and Switzerland. The technical program of the workshop included an invited talk, presentations of refereed and accepted papers and system descriptions, as well as non-refereed system demonstrations and poster presentations. The contributions in this volume were reviewed by at least two referees. We would like to thank all authors who submitted papers and all workshop participants for their fruitful discussions. We are grateful to the members of the program committee and of the local organisation as well as to the referees. We would like to express our thanks to the Society of Logic Programming (GLP e.V.) for handling finances and the University of Ulm for hosting the workshop.

Handbook of Combinatorial Optimization, 2013

The Satisfiability problem (SAT) has gained considerable attention over the past decade for two reasons. First, the performance of competitive SAT solvers has improved enormously due to the implementation of new algorithmic concepts. Second, so many real-world problems that are not naturally expressed as instances of SAT can be transformed to SAT instances and solved relatively efficiently using one of the ever improving SAT solvers or solvers based on SAT. This chapter attempts to clarify these successes by presenting the important advances in SAT algorithm design as well as the classic implementations of SAT solvers. Some applications to which SAT solvers have been successfully applied are also presented. The first section of the chapter presents some logic background and notation that will be necessary to understand and express the algorithms presented. The second section presents several representations for SAT instances in preparation for discussing the wide variety of SAT solver implementations that have been tried. The third section presents some applications of SAT. The final two sections presents algorithms for SAT, including search and heuristic algorithms plus systems that use SAT to manage the logic of complex computations.

2017

Here, we present a family of complete interleaving depth-first search strategies for embedded, domain-specific logic languages. We derive our search family from a stream-based implementation of incomplete depth-first search. The DSL’s programs’ texts induce particular strategies guaranteed to be complete. 1998 ACM Subject Classification D.3.2 Language Classifications: Applicative (functional) languages, Constraint and logic languages