Operational Semantics of Resolution and Productivity in Horn Clause Logic

This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by term-matching, the recently introduced structural resolution, and partial (or lazy) resolution. We express them all uniformly as abstract reduction systems, which allows us to undertake a thorough comparative analysis of their properties. To match this small-step semantics, we propose to take Howard's System H as a type-theoretic semantic counterpart. Using System H, we interpret Horn formulas as types, and a derivation for a given formula as the proof term inhabiting the type given by the formula. We prove soundness of these abstract reduction systems relative to System H, and we show completeness of SLD-resolution and structural resolution relative to System H. We identify conditions under which structural resolution is operationally equivalent to SLD-resolution. We show correspondence between term-matching resolution for Horn clause programs without existential variables and term rewriting.Comment: Journal Formal Aspect of Computing, 201

An interactive semantics of logic programming

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory and Practice of Logic Programmin

COSMICAH 2005: workshop on verification of COncurrent Systems with dynaMIC Allocated Heaps (a Satellite event of ICALP 2005) - Informal Proceedings

Lisboa Portugal, 10 July 200

Rewriting Logic Semantics of a Plan Execution Language

The Plan Execution Interchange Language (PLEXIL) is a synchronous language developed by NASA to support autonomous spacecraft operations. In this paper, we propose a rewriting logic semantics of PLEXIL in Maude, a high-performance logical engine. The rewriting logic semantics is by itself a formal interpreter of the language and can be used as a semantic benchmark for the implementation of PLEXIL executives. The implementation in Maude has the additional benefit of making available to PLEXIL designers and developers all the formal analysis and verification tools provided by Maude. The formalization of the PLEXIL semantics in rewriting logic poses an interesting challenge due to the synchronous nature of the language and the prioritized rules defining its semantics. To overcome this difficulty, we propose a general procedure for simulating synchronous set relations in rewriting logic that is sound and, for deterministic relations, complete. We also report on two issues at the design level of the original PLEXIL semantics that were identified with the help of the executable specification in Maude

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

A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc