HORNLOG: A graph-based interpreter for general Horn clauses

AbstractThis paper presents hornlog, a general Horn-clause proof procedure that can be used to interpret logic programs. The system is based on a form of graph rewriting, and on the linear-time algorithm for testing the unsatisfiability of propositional Horn formulae given by Dowling and Gallier [8]. hornlog applies to a class of logic programs which is a proper superset of the class of logic programs handled by PROLOG systems. In particular, negative Horn clauses used as assertions and queries consisting of disjunctions of negations of Horn clauses are allowed. This class of logic programs admits answers which are indefinite, in the sense that an answer can consist of a disjunction of substitutions. The method does not use the negation-by- failure semantics [6] in handling these extensions and appears to have an immediate parallel interpretation

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Łukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules – a syntactic generalization which does not affect the expressivity of ASP in the classical case – the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully characterizing the complexity of FASP in this more general setting is not likely to have an easy solution

Relational semantics of linear logic and higher-order model-checking

In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church encoding of any higher-order recursion scheme (HORS) comes together with a dual Church encoding of an alternating tree automata (ATA) of the same signature. Moreover, the interaction between the relational interpretations of the HORS and of the ATA identifies the set of accepting states of the tree automaton against the infinite tree generated by the recursion scheme. We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities) in higher-order model-checking. We show in particular how to reunderstand in this way the type-theoretic approach to higher-order model-checking developed by Kobayashi and Ong. We briefly explain in the end of the paper how his analysis driven by linear logic results in a new and purely semantic proof of decidability of the formulas of the monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte

A Denotational Semantics for First-Order Logic

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL 2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc

Model Checking Linear Logic Specifications

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear logic programming language called LO enriched with universally quantified goal formulas. Although LO was originally introduced as a theoretical foundation for extensions of logic programming languages, it can also be viewed as a very general language to specify a wide range of infinite-state concurrent systems. Our approach is based on the relation between backward reachability and provability highlighted in our previous work on propositional LO programs. Following this line of research, we define here a general framework for the bottom-up evaluation of first order linear logic specifications. The evaluation procedure is based on an effective fixpoint operator working on a symbolic representation of infinite collections of first order linear logic formulas. The theory of well quasi-orderings can be used to provide sufficient conditions for the termination of the evaluation of non trivial fragments of first order linear logic.Comment: 53 pages, 12 figures "Under consideration for publication in Theory and Practice of Logic Programming

Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm