Andrea Formisano

A comparison of CLP(FD) and ASP solutions to NP-Complete problems

This paper presents experimental comparisons between declarative encodings of various computationally hard problems in both Answer Set Programming (ASP) and Constraint Logic Programming (CLP) over finite domains. The objective is to identify how the solvers in the two domains respond to different problems, highlighting strengths and weaknesses of their implementations and suggesting criteria for choosing one approach versus the other. Ultimately, the work in this paper is expected to lay the ground for transfer of concepts between the two domains (e.g., suggesting ways to use CLP in the execution of ASP).

An empirical study of constraint logic programming and answer set programming solutions of combinatorial problems

This paper presents experimental comparisons between the declarative encodings of various computationally hard problems in Answer Set Programming (ASP) and Constraint Logic Programming over Finite Domains (CLP(FD)). The objective is to investigate how solvers in the two domains respond to different problems, highlighting the strengths and weaknesses of their implementations, and suggesting criteria for choosing one approach over the other. Ultimately, the work in this paper is expected to lay the foundations for a transfer of technology between the two domains, for example by suggesting ways to use CLP(FD) in the execution of ASP. †A preliminary version of this paper appeared in the Proceedings of the International Conference on Logic Programming, 2005, pp. 67–82.

Answer Set Programming with Resources

In this article, we propose an extension of Answer Set Programming (ASP) to support declarative reasoning on consumption and production of resources. We call the proposed extension RASP, standing for ‘Resourced ASP’. Resources are modeled by introducing special atoms, called amount-atoms, to which we associate quantities that represent the available amount of a certain resource. The ‘firing’of aRASP rule involving amount-atoms can both consume and produce resources. A RASP rule can be fired several times, according to its definition and to the available quantities of required resources. We define the semantics for RASP programs by extending the usual answer set semantics. Different answer sets correspond to different possible allocations of available resources. We then propose an implementation based on standard ASP-solvers. The implementation consists of a standard translation of each RASP rule into a set of plain ASP-rules and of an inference engine that manages the firing of RASP rules.

An Equational Re-engineering of Set Theories

New successes in dealing with set theories by means of stateof-the-art theorem-provers may ensue from terse and concise axiomatizations, such as can be moulded in the framework of the (fully equational) Tarski-Givant map calculus. In this paper we carry out this task in detail, setting the ground for a number of experiments.

Extending and Implementing RASP

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.

An efficient relational deductive system for propositional non-classical logics

We describe a relational framework that uniformly supports formalization and automated reasoning in varied propositional modal logics. The proof system we propose is a relational variant of the classical Rasiowa-Sikorski proof system. We introduce a compact graph-based representation of formulae and proofs supporting an efficient implementation of the basic inference engine, as well as of a number of refinements. Completeness and soundness results are shown and a Prolog implementation is described.

CUD@SAT: SAT solving on GPUs

The parallel computing power offered by graphic processing units (GPUs) has been recently exploited to support general purpose applications – by exploiting the availability of general API and the single-instruction multiple-thread-style parallelism present in several classes of problems (e.g. numerical simulations and matrix manipulations) – where relatively simple computations need to be applied to all items in large sets of data. This paper investigates the use of GPUs in parallelising a class of search problems, where the combinatorial nature leads to large parallel tasks and relatively less natural symmetries. Specifically, the investigation focuses on the well-known satisfiability testing (SAT) problem and on the use of the NVIDIA compute unified device architecture, one of the most popular platforms for GPU computing. The paper explores ways to identify strong sources of GPU-style parallelism from SAT solving. The paper describes experiments with different design choices and evaluates the results. The outcomes demonstrate the potential for this approach, leading to one order of magnitude of speedup using a simple NVIDIA platform.

Theory-specific automated reasoning

In designing a large-scale computerized proof system, one is often confronted with issues of two kinds: issues regarding an underlying logical calculus, and issues that refer to theories, either specified axiomatically or characterized by indication of either a privileged model or a family of intended models. Proof services related to the theories most often take the form of satisfiability decision or semi-decision procedures (in a sense, polyadic inference rules), while some of the services offered by the calculus (e.g., the Davis-Putnam propositional satisfiability checker) provide low-level mechanisms for integrating services of the former kind. Integration among services can ensure speed-up (i.e., lower number of steps) in the proofs, but it must always be legitimatized by a conservativeness result. Interoperability among proof checkers and autonomous theorem provers is another key point of integration. In discussing these and related issues, this paper refers to Set Theory as the unifying background, and to a specific proof-checker based on a slightly unorthodox formalization of it as an arena for experimentation.

Multivalued action languages with constraints in CLP(FD)

Action description languages, such as A and B [6], are expressive instruments introduced for formalizing planning domains and problems. The paper starts by proposing a methodology to encode an action language (with conditional effects and static causal laws), a slight variation of B, using Constraint Logic Programming over Finite Domains. The approach is then generalized to lift the use of constraints to the level of the action language itself. A prototype implementation has been developed, and the preliminary results are presented and discussed.

Layered map reasoning: An experimental approach put to trial on sets

Abstract New successes in dealing with set-theories by means of state-of-the-art theorem-provers may ensue from terse and concise axiomatic systems, such as can be moulded in the framework of the (fully equational) Tarski-Givant formalism of dyadic relations, here named ‘maps’. This paper sets the ground for systematic experimentation based on such axiomatic systems. On top of a kernel axiomatization of map algebra, we develop a layered formalization of basic set-theoretic concepts. A number of concrete experiments have been carried out in this framework, as the paper reports, with the assistance of a first-order theorem-prover. The aim is to assess the potential usefulness of the proposed layered architecture and, to the extent it reveals promising, to best tune it.