Extremal problems in logic programming and stable model computation

We study the following problem: given a class of logic programs C, determine the maximum number of stable models of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at most n. We also characterize the programs for which the maxima are attained. We obtain similar results for the class of all disjunctive logic programs with at most n clauses, each of length at most m, and for the class of all disjunctive logic programs of size at most n. Our results on logic programs have direct implication for the design of algorithms to compute stable models. Several such algorithms, similar in spirit to the Davis-Putnam procedure, are described in the paper. Our results imply that there is an algorithm that finds all stable models of a program with n clauses after considering the search space of size O(3^{n/3}) in the worst case. Our results also provide some insights into the question of representability of families of sets as families of stable models of logic programs

Reasoning with Stratified Default Theories

Default logic is one of the principal formalisms for nonmonotonic reasoning. In this paper, we study algorithms for computing extensions for a class of general propositional default theories. We focus on the problem of partitioning a given set of defaults into a family of its subsets. Then we investigate how the results obtained for these subsets can be put together to achieve the extensions of the original theory. The method we propose is designed to prune the search space and reduce the number of calls to propositional provability procedure. It also constitutes a simple and uniform framework for the design of parallel algorithms for computing extensions

Towards Programming in Default Logic

In this paper we describe a fragment of default logic suitable for encoding problems from other domains. We investigate a subclass of first order open default theories, which we call extensional default theories. This class of default theories allows easy and compact encodings of problems for experimenting with default reasoning systems. Because most existing systems for default reasoning assume that all input defaults are closed or propositional we show how to transform an extensional default theory to a closed first order default theory or a propositional default theory with same extensions. Finally, we present several encodings of known graph problems in the language of extensional default theories. These encodings can be regarded as benchmark problems for experimenting with nonmonotonic reasoning systems. 1 Introduction In this paper we develop a simple first order nonmonotonic reasoning formalism for describing combinatorial problems Our framework is based on default log..

Extremal Problems in Logic Programming and Stable Model Computation

We study the following problem: given a class of (disjunctive) logic programs C, determine the maximum number of stable models (answer sets) of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at most n. We also characterize the programs for which the maxima are attained. We obtain similar results for the class of all disjunctive logic programs with at most n clauses, each of length at most m, and for the class of all disjunctive logic programs of size at most n. Our results on logic programs have direct implication for the design of algorithms to compute stable models. Several such algorithms, similar in spirit to the Davis-Putnam procedure, are described in the paper. 1 Introduction In this paper we study extremal problems appearing in the context of finite propositional logic programs. Specifically, we consider the following problem: given a class of logic programs C, determine th..

Default Reasoning System DeReS

In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one or all extensions. If an input theory is a logic program, DeReS computes stable models of this program and supports queries on membership of an atom in some or all stable models. The paper contains an account of our preliminary experiments with DeReS and a discussion of the results. We show that a choice of a propositional prover is critical for the efficiency of DeReS. We also present a general technique that eliminates the need for some global consistency checks and results in substantial speedups. We experimentally demonstrate the potential of the concept of relaxed stratification for making automated reasoning systems practical. 1 INTRODUCTION The area of nonmonotonic l..

Computing With Default Logic

Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of large-scale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i..

Dual-time-point PET/CT study protocol can improve the larynx cancer diagnosis

AimTo evaluate whether the sequential dual-time-point fluorine-18-fluorodeoxyglucose positron emission tomography/computed tomography (DTP 18F-FDG PET/CT) study improves the differential diagnosis in the larynx.BackgroundIn some cases, the clinical and metabolic similarity of laryngitis and larynx cancer make differential diagnostics difficult when performing standard 18F-FDG PET/CT examinations; therefore, an additional study protocol performance seems to be of reasonable value.Materials and methods90 patients (mean age: 61±11 years, range: 41–84 years): 23 women (mean age: 63±10 years, range: 51–84 years) and 67 men (mean age: 61±11 years, range: 41–80 years) underwent delayed 18F-FDG PET/CT examinations at 60 and 90min post intravenous injection (p.i.) of the radiopharmaceutical 18F-FDG. We compared the metabolic activity of 90 structures divided into following groups: normal larynx (30 patients), laryngitis (30 lesions) and larynx cancer (30 tumors) with maximal and mean standardized uptake value (SUVmax, SUVmean) and the retention index (RI-SUVmax). We used the receiver operating characteristics (ROC) curve to evaluate the SUVmax cut-off values.ResultsThe SUVmax cut-off value at 60 and 90min p.i. of 2.3 (sensitivity/specificity: 96.4%/100%) and 2.4 (94.2%/100%), respectively, distinguished normal and abnormal metabolic activity in the larynx. When laryngitis and tumors were compared, the SUVmax cut-off values obtained after initial and delayed imaging were 3.6 (87.5%/52.0%) and 6.1 (58.3%/84%), respectively. The RI-SUVmax of 1.3% (71.4%/88.1%) suggested abnormality, while RI-SUVmax of 6.6%, malignant etiology (75.0%/80.0%).ConclusionsIn this study, the sequential DTP scanning protocol improved the sensitivity and specificity of the PET/CT method in terms of differential diagnosis within the larynx