On computing logic programs

In this paper we present and compare some classical problem-solving methods for computing the stable models of logic programs with negation. Using a graph theoretic representation of logic programs and their stable models, we discuss and compare linear programming, propositional satisfiability, constraint satisfaction, and graph methods.     

Complexity analysis of propositional concurrent programs using domino tiling

The complexities of the possible rendezvous and the lockout problems for propositional concurrent programs are investigated in detail. We develop a unified strategy, based on domino tiling, to show that the above two problems with respect to a variety of propositional concurrent programs are complete for a broad spectrum of complexity classes, ranging from NLOGSPACE, PTIME, NP, PSPACE to EXPTIME. Our technique is novel in the sense that it demonstrates how two seemingly unrelated models, namely, propositional concurrent programs and dominoes, can be linked together in a natural and elegant fashion.     

Transforming equality logic to propositional logic

We investigate and compare various ways of transforming equality formulas to propositional formulas, in order to be able to solve satisfiability in equality logic by means of satisfiability in propositional logic. We propose equality substitution as a new approach combining desirable properties of earlier methods, we prove its correctness and show its applicability by experiments.     

An extended Petri net model for normal logic programs

This paper presents an application of the concepts of siphons (deadlocks) and inhibitor arcs in Petri net theory to logic programs with negations. More specifically, an extended Petri net is used to model function-free normal logic programs. In this model, because of the presence of inhibitor arcs, the arbitrary applications of firing rule may cause a contradictory situation. We suggest two directions to avoid contradictions: greedy and secure applications of firing rule. We choose the secure application and show that this is a direct translation of the well-founded semantics in the net model. Furthermore, we show that the greatest unfounded set corresponds to the greatest siphon in Petri net theory when we delete the transitions disabled by the secure application of firing rule, and that the property of siphon simplifies the computation of well-founded semantics for logic programs. We also propose the reduced-Petri-net method by which we can reduce an extended Petri net to a Petri net without inhibitor arcs and compute the well-founded model by iterative applications of this transformation using conventional application of firing rule     

Symbolic backward reachability with effectively propositional logic

We describe a symbolic procedure for solving the reachability problem of transition systems that use formulae of Effectively Propositional Logic to represent sets of backward reachable states. We discuss the key ideas for the mechanization of the procedure where fix-point checks are reduced to SMT problems. We also show the termination of the procedure on a sub-class of transition systems. Then, we discuss how reachability problems for this sub-class can be used to encode analysis problems of administrative policies in the Role-Based Access Control (RBAC) model that is one of the most widely adopted access control paradigms. An implementation of a refinement of the backward reachability procedure, called asasp, shows better flexibility and scalability than a state-of-the-art tool on a significant set of security problems.     

Expressiveness of propositional projection temporal logic with star

This paper investigates the expressiveness of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Büchi automata and ω-regular expressions are first extended as Stutter Büchi Automata (SBA) and Extended Regular Expressions (ERE) to include both finite and infinite strings. Further, by equivalent transformations among PPTL* formulas, SBAs and EREs, PPTL* is proved to represent exactly the full regular language. Moreover, some fragments of PPTL* are characterized, and finally, PPTL* and its fragments are classified into five different language classes.     

Dempster-shafer approach in propositional logic

A general framework of uncertainty reasoning based on Dempster-Shafer's theory is proposed in the context of logic calculus. Under this framework, any inference can be conducted without much computational complexity. Furthermore, it avoids the problems of considering conflicting information and common universe when two pieces of evidence are combined. © 1993 John Wiley & Sons, Inc.     

Reducts of propositional theories,satisfiability relations,and generalizations of semantics of logic programs

Over the years, the stable-model semantics has gained a position of the correct (two-valued) interpretation of default negation in programs. However, for programs with aggregates (constraints), the stable-model semantics, in its broadly accepted generalization stemming from the work by Pearce, Ferraris and Lifschitz, has a competitor: the semantics proposed by Faber, Leone and Pfeifer, which seems to be essentially different. Our goal is to explain the relationship between the two semantics. Pearce, Ferraris and Lifschitz's extension of the stable-model semantics is best viewed in the setting of arbitrary propositional theories. We propose here an extension of the Faber–Leone–Pfeifer semantics, or FLP semantics, for short, to the full propositional language, which reveals both common threads and differences between the FLP and stable-model semantics. We use our characterizations of FLP-stable models to derive corresponding results on strong equivalence and on normal forms of theories under the FLP semantics. We apply a similar approach to define supported models for arbitrary propositional theories, and to study their properties.     

Equivalence of propositional Prolog programs

We show that the equivalence problem for propositional Prolog programs is coNP-complete. Considering yes-no answers only the modified equivalence problem is solvable in polynomial time. Furthermore, the problem whether a program does not terminate for some question is NP-complete. For a fixed question the loop problem can be decided in linear time.The work of this author was supported by the Studienstiftung des Deutschen Volkes.     

An extended variant of atoms loop check for positive logic programs

The Equality check and the Subsumption check are weakly sound, but are not complete even for function-free logic programs. Although the OverSize (OS) check is complete for positive logic programs, it is too general in the sense that it prunes SLD-derivations merely based on the depth-bound of repeated predicate symbols and the size of atoms, regardless of the inner structure of the atoms, so it may make wrong conclusions even for some simple programs. In this paper, we explore complete loop checking mechanisms for positive logic programs. We develop an extended Variant of Atoms (VA) check that has the following features: (1) it generalizes the concept of “variant” from “the same up to variable renaming” to “the same up to variable renaming except possibly with some arguments whose size recursively increases”, (2) it makes use of the depth-bound of repeated variants of atoms instead of depth-bound of repeated predicate symbols, (3) it combines the Equality/Subsumption check with the VA check, (4) it is complete w. r. t. the leftmost selection rule for positive logic programs, and (5) it is more sound than both the OS check and all the existing versions of the VA check. The research was completed when the author visited the University of Maryland Institute for Advanced Computer Studies. Yi-Dong Shen, Ph. D: He is a professor of Computer Science at Chongqing University, China. He received the Ph. D degree in computer Science from Chongqing University in 1991. He was a visiting researcher at the University of Valenciennes, France (1992–1993) and the University of Maryland Institute for Advanced Computer Studies (UMIACS), U. S. A. (1995–1996), respectively. His present interests include: Artificial Intelligence, Deductive and Object-Oriented Databases, Logic Programming and Parallel Processing.     

Sequential method in propositional dynamic logic

Summary Recently prepositional modal logic of programs, called prepositional dynamic logic, has been developed by many authors, following the ideas of Fisher and Ladner [1] and Pratt [12]. The main purpose of this paper is to present a Gentzen-type sequential formulation of this logic and to establish its semantical completeness with due regard to sequential formulation as such. In a sense our sequential formulation might be regarded as a powerful tool to establish the completeness theorem of already familiar axiomatizations of prepositional dynamic logic such as seen in Harel [4], Parikh [11] or Segerberg [15]. Indeed our method is powerful enough in completeness proof to yield a desired structure directly without making a detour through such intermediate constructs as a pseudomodel or a nonstandard structure, which can be seen in Parikh [11]. We also show that our sequential system of prepositional dynamic logic does not enjoy the so-called cut-elimination theorem.     

Equivalent logic programs and symmetric homogeneous forms of logic programs with equality

This article introduces the notion of CAS-equivalent logic programs: logic programs with identical correct answer substitutions. It is shown that the notions CAS-equivalence, refutational equivalence, and logical equivalence do not coincide in the case of definite clause logic programs. Least model criteria for refutational and CAS-equivalence are suggested and their correctness is proved. The least model approach is illustrated by two proofs of CAS-equivalence. It is shown that the symmetric extension of a logic program subsumes the symmetry axiom and the symmetric homogeneous form of a logic program with equality subsumes the symmetry, transitivity, and predicate substitutivity axioms of equality. These results contribute towards the goal of building equality into standard Prolog without introducing additional inference rules.     

Reasoning with propositional knowledge based on fuzzy neural logic

In this article, a new kind of reasoning for propositional knowledge, which is based on the fuzzy neural logic initialed by Teh, is introduced. A fundamental theorem is presented showing that any fuzzy neural logic network can be represented by operations: bounded sum, complement, and scalar product. Propositional calculus of fuzzy neural logic is also investigated. Linear programming problems risen from the propositional calculus of fuzzy neural logic show a great advantage in applying fuzzy neural logic to answer imprecise questions in knowledge-based systems. An example is reconsidered here to illustrate the theory. © 1996 John Wiley & Sons, Inc.     

Syntax theory of finite lattice-valued propositional logic

In this paper,we establish the graded syntax theory of lattice-valued propositional logic based on finite lattice implication algebras,define the notions of syntactic consequence operation and formal proof,and develop a kind of graded finite lattice-valued propositional calculus.By generalizing classic provable equivalence relation,we present a kind of generalized provable equivalence relation,and establish the corresponding quotient algebra.Finally,we establish the generalized deduction theorem by syntactic consequence operation,and establish the completeness in Pavelka’s sense based on finite chains.