Herod and Pilate: Two Tableau Provers for Basic Hybrid Logic

International audienceThis work presents two provers for basic hybrid logic HL(@), which have been implemented with the aim of comparing the internalised tableau calculi independently proposed, respectively, by Bolander and Blackburn [3] and Cerrito and Cialdea Mayer [5]. Experimental results are reported, evaluating, from the practical point of view, the different treatment of nominal equalities of the two calculi

A New General Method to Generate Random Modal Formulae for Testing Decision Procedures

The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF_[]m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests

A New General Method to Generate Random Modal Formulae for Testing Decision Procedures

The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF_[]m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests

Tableaux clausal para lógica modal

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2016.Este trabalho apresenta a definição de um cálculo tableaux clausal proposto para lógicas modais, além de apresentar uma implementação do mesmo. O objetivo geral é aplicar o método refutacional tableaux utilizando a forma normal construída para resolução clausal na tentativa de gerar o máximo de informações possíveis sobre conjuntos de fórmulas na linguagem modal, sem que seja necessário a especificação de um número elevado de regras de inferência no cálculo, o que tornaria a tarefa de implementar razoavelmente mais difícil. Estas informações extraídas contêm singularidades dos conjuntos de fórmulas que podem auxiliar em decisões relacionadas aos métodos de provas aplicados aos mesmos. As provas de correção para o cálculo são apresentadas. A implementação realizada, apesar de bem sucedida, revelou imperfeições com relação ao desempenho de execução. Esforços direcionados à melhoria de tais imperfeições, bem como uma análise das informações extraídas, são deixados como trabalhos futuros.This work presents a clausal tableaux calculus for modal logics and na implementation for it. The main goal is to combine aspects of two different proof methods, the inference rules of a tableaux calculus and the normal form employed in a clausal resolution method. The goal is to generate as much information as possible about sets of formulae in modal logic, without the need to define a large number of inference rules in the calculus, which would make the job of implementing the calculus reasonably harder. The pieces of extracted information may help to characterise singularities of the set of formulae, which could then help to make decisions about what proof method to apply to such a set. The implementation is correct, but does not perform well. Efforts in the direction of a more robust implementation and the analysis of the extracted information are left as future work

A Benchmark Method for the Propositional Modal Logics K, KT, S4

A lot of methods have been proposed (and sometimes implemented) for proof search in the propositional modal logics K, KT, and S4. It is difficult to compare the usefulness of these methods in practice, since mostly only the execution times for a few simple formulas have been published. We try to improve this unsatisfactory situation by presenting a set of benchmark formulas. Note that we do not just list formulas, but give a method that allows to compare different provers today and in the future. As a starting point we give the results we obtained when we applied this benchmark method to the Logics Workbench (LWB). Moreover we hope that the discussion of postulates concerning benchmark tests for automated theorem provers help to obtain improved benchmark methods for other logics, too

Hypertableau Reasoning for Description Logics

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies