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Negation as a Resource: a Novel View on Answer Set Semantics

Costantini S., Formisano A.

Fundamenta Informaticae

2015

Vol. 140, nr 3/4

279--305

In recent work, we provided a formulation of ASP programs in terms of linear logic theories. Answer sets were characterized in terms of maximal tensor conjunctions provable from such theories. In this paper, we propose a full comparison between Answer Set Semantics and its variation obtained by interpreting literals (including negative literals) as resources, which leads to a different interpretation of negation. We argue that this novel view can be of both theoretical and practical interest, and we propose a modified Answer Set Semantics that we call Resource-based Answer Set Semantics. An advantage is that of avoiding inconsistencies, as every program has a (possibly empty) resource-based answer set. This implies however the introduction of a different way of representing constraints. We provide a characterization of the new semantics as a variation of the answer set semantics, and also in terms of Autoepistemic Logic. The latter characterization leads to a way of computing resource-based answer set via answer set solvers.

Nested Weight Constraints in ASP

Costantini S., Formisano A.

Fundamenta Informaticae

2013

Vol. 124, nr 4

449--464

Weight constraints are a powerful programming construct that has proved very useful within the Answer Set Programming paradigm. In this paper, we argue that practical Answer Set Programming might take profit from introducing some forms of nested weight constraints. We define such empowered constraints (that we call 'Nested Weight Constraints') and discuss their semantics and their complexity.

Extending and Implementing RASP

Costantini S., Formisano A., Petturiti D.

Fundamenta Informaticae

2011

Vol. 105, nr 1/2

1-33

In previous work we have proposed an extension to ASP (Answer Set Programming), called RASP, standing for ASP with Resources. RASP supports declarative reasoning on production and consumption of (amounts of) resources. The approach combines answer set semantics with quantitative reasoning and relies on an algebraic structure to support computations and comparisons of amounts. The RASP framework provides some form of preference reasoning on resources usage. In this paper, we go further in this direction by introducing expressive constructs for supporting complex preferences specification on aggregate resources. We present a refinement of the semantics of RASP so as to take into account the new constructs. For all the extensions, we provide an encoding into plain ASP.We prove that the complexity of establishing the existence of an answer set, in such an enriched framework, remains NP-complete as in ASP. Finally, we report on raspberry, a prototypical implementation of RASP. This tool consists of a compiler that, given a ground RASP program, produces a pure ASP encoding suitable to be processed by commonly available ASP-solvers.