The topics of structural proof theory and logic programming have influenced each other for more than three decades. Proof theory has contributed the notion of sequent calculus, linear logic, and higher-order quantification. Logic programming has introduced new normal forms of proofs and forced the examination of logic-based approaches to the treatment of bindings. As a result, proof theory has responded by developing an approach to proof search based on focused proof systems in which introduction rules are organized into two alternating (...) phases of rule application. Since the logic programming community can generate many examples and many design goals, the close connections with proof theory have helped to keep proof theory relevant to the general topic of computational logic. (shrink)

RASP is a recent extension to Answer Set Programming (ASP) that permits declarative specification and reasoning on the consumption and production of resources. ASP can be seen as a particular case of RASP. In this paper, we study the relationship between linear logic and RASP problem specification. We prove that RASP programs can be translated into (a fragment of) linear logic, and vice versa. In doing so, we introduce a linear logic representation of default negation as understood in ASP. We (...) are also able to establish a link between linear logic and here-and-there (HT) logic. (shrink)

A Linear Logic automaton is a hybrid of a finite automaton and a non-deterministic Petri net. LL automata commands are represented by propositional Horn Linear Logic formulas. Computations performed by LL automata directly correspond to cut-free derivations in Linear Logic.A programming language of LL automata is developed in which typical sequential, non-deterministic and parallel programming constructs are expressed in the natural way.All non-deterministic computations, e.g. computations performed by programs built up of guarded commands in the Dijkstra's approach to non-deterministic programming, (...) are directly simulated within the framework of Linear Logic automata, and thereby within the Horn framework of Linear Logic. (shrink)