72 research outputs found
Paracomplete logic Kl: natural deduction, its automation, complexity and applications
In the development of many modern software solutions where the underlying systems are complex, dynamic and heterogeneous, the significance of specification-based verification is well accepted. However, often parts of the specification may not be known. Yet reasoning based on such incomplete specifications is very desirable. Here, paracomplete logics seem to be an appropriate formal setup: opposite to Tarski’s theory of truth with its principle of bivalence, in these logics a statement and its negation may be both untrue. An immediate result is that the law of excluded middle becomes invalid. In this paper we show a way to apply an automatic proof searching procedure for the paracomplete logic Kl to reason about incomplete information systems. We provide an original account of complexity of natural deduction systems, leading us closer to the efficiency of the presented proof search algorithm. Moreover, we have turned the assumptions management into an advantage showing the applicability of the proposed technique to assume-guarantee reasoning
Strong Completeness Results for Paraconsistent Logic Programming
In [6], we introduced a means of allowing logic programs to contain negations in both the head and the body of a clause. Such programs were called generally Horn programs (GHPs, for short). The model-theoretic semantics of GHPs were defined in terms of four-valued Belnap lattices [5]. For a class of programs called well-behaved programs, an SLD-resolution like proof procedure was introduced. This procedure was proven (under certain restrictions) to be sound (for existential queries) and complete (for ground queries). In this paper, we remove the restriction that programs be well-behaved and extend our soundness and completeness results to apply to arbitrary existential queries and to arbitrary GHPs. This is the strongest possible completeness result for GHPs. The results reported here apply to the design of very large knowledge bases and in processing queries to knowledge bases that possibly contain erroneous information
Tackling Incomplete System Specifcations Using Natural Deduction in the Paracomplete Setting
In many modern computer applications the significanceofspecificationbasedverificationiswellaccepted.However, when we deal with such complex processes as the integration of heterogeneous systems, parts of specification may be not known. Therefore it is important to have techniques that are able to cope with such incomplete information. An adequate formal set up is given by so called paracomplete logics, where, contrary to the classical framework, for some statements we do not have evidence to conclude if they are true or false. As a consequence, for example, the law of excluded middle is not valid. In this paper we justify how the automated proof search technique for paracomplete logic PComp can be efficiently applied to the reasoning about systems with incomplete information. Note that for many researchers, one of the core features of natural deduction, the opportunity to introduce arbitrary formulae as assumptions, has been a point of great scepticism regarding the very possibility of the automation of the proof search. Here, not only we show the contrary, but we also turned the assumptions management into an advantage showing the applicability of the proposed technique to assume-guarantee reasoning. Keywords - incomplete information, automated natural deduction, paracomplete logic, requirements engineering, assumeguarantee reasoning, component based system assembly
Paraconsistência em lógica híbrida
Mestrado em Matemática e AplicaçõesThe use of hybrid logics allows the description of relational structures, at the
same time that allows establishing accessibility relations between states and,
furthermore, nominating and making mention to what happens at speci c
states.
However, the information we collect is subject to inconsistencies, namely,
the search for di erent information sources can lead us to pick up contradictions.
Nowadays, by having so many means of dissemination available,
that happens frequently.
The aim of this work is to develop tools capable of dealing with contradictory
information that can be described as hybrid logics' formulas. To build
models, to compare inconsistency in di erent databases, and to see the applicability
of this method in day-to-day life are the basis for the development
of this dissertation.O uso de lógicas híbridas permite a descrição de estruturas relacionais, ao mesmo tempo que permite estabelecer relações de acessibilidade entre
estados, e, para além disso, nomear e fazer referência ao que acontece em
estados específicos.
No entanto, a informação que recolhemos está sujeita a inconsistências,
isto é, a procura de diferentes fontes de informação pode levar a recolha
de contradições. O que nos dias de hoje, com tantos meios de divulgação
disponíveis, acontece frequentemente.
O objetivo deste trabalho e desenvolver ferramentas capazes de lidar com informação contraditória que possa ser descrita através de fórmulas de lógicas
híbridas. Construir modelos e comparar a inconsistência de diferentes bases
de dados e ver a aplicabilidade deste método no dia-a-dia são a base para
o desenvolvimento desta dissertação
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