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An effective fixpoint semantics for linear logic programs

Published online by Cambridge University Press:  18 December 2001

MARCO BOZZANO ,
GIORGIO DELZANNO  and
MAURIZIO MARTELLI
MARCO BOZZANO
Affiliation:
Dipartimento di Informatica e Scienze dell'Informazione, Università di Genova, Via Dodecaneso 35, 16146 Genova - Italy; (e-mail: bozzano@disi.unige.it, giorgio@disi.unige.it, martelli@disi.unige.it)
GIORGIO DELZANNO
Affiliation:
Dipartimento di Informatica e Scienze dell'Informazione, Università di Genova, Via Dodecaneso 35, 16146 Genova - Italy; (e-mail: bozzano@disi.unige.it, giorgio@disi.unige.it, martelli@disi.unige.it)
MAURIZIO MARTELLI
Affiliation:
Dipartimento di Informatica e Scienze dell'Informazione, Università di Genova, Via Dodecaneso 35, 16146 Genova - Italy; (e-mail: bozzano@disi.unige.it, giorgio@disi.unige.it, martelli@disi.unige.it)
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Abstract

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

Keywords

program analysisBoolean functions
Type
Research Article
Information
Theory and Practice of Logic Programming , Volume 2 , Issue 1 , January 2002 , pp. 85 - 122
Copyright
© 2002 Cambridge University Press

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