Analytic fuzzy tableaux

 In this paper Beth–Smullyan's tableaux method is extended to the fuzzy propositional logic. The fuzzy tableaux method is based on the concepts of t-truth and extended graded formula. As in classical logic, it is a refutation procedure. A closed fuzzy tableau beginning with the extended graded formula [r, A] asserting that this is not t-true, is a tableau proof of the graded formula (A, r). The theorems of soundness, completeness, and decidability are proved.     

Lighting Up

Through the work of London practice Cinimod Studio, led by Dominic Harris, Valentina Croci explores the potential that lighting design offers for interactive work, whether it is transforming unwelcoming urban spaces or enhancing the public's experience of the city. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimization techniques for propositional intuitionistic logic and their implementation

This paper presents some techniques which bound the proof search space in propositional intuitionistic logic. These techniques are justified by Kripke semantics and are the backbone of a tableau based theorem prover (PITP) implemented in C++. PITP and some known theorem provers are compared using the formulas of ILTP benchmark library. It turns out that PITP is, at the moment, the propositional prover that solves most formulas of the library.     

Incremental variable splitting

The variable splitting method for free-variable tableau calculi provides an admissibility condition under which the same free variables can be assigned values independently on different branches. While this has a large potential for automated proof search, a direct implementation of this condition is impractical. We adapt the incremental closure framework for free variables to variable splitting tableaux by recasting the admissibility condition for closing substitutions into a constraint satisfaction problem. The resulting mechanism allows to check the existence of an admissible closing substitution incrementally during the construction of a proof. We specify a rule-based algorithm for testing satisfiability of constraints that accounts for split variables, and present experimental results based on a prototype variable splitting theorem prover implementation measuring the computational overhead of the variable splitting framework.     

基于形式概念分析的粗糙描述逻辑研究

以往的粗糙描述逻辑(RDL)都是基于传统的粗糙集理论。实际上,经常会出现用形式概念表示一个概念的情况,此时一个自然的问题就是如何处理可能出现的不确定概念。把形式概念分析与粗糙集理论联系起来做为基础,给出可定义概念和不可定义概念的定义,并给出不可定义概念的上近似和下近似,这里的近似定义虽然不同于传统的粗糙近似算子形式,但是有很好的实用性。基于新的上下近似定义,把一组近似算子引入到描述逻辑的结构中,形成一种新的粗糙描述逻辑。给出了相应的语法和语义,最后还给出了扩展的Tableau算法,可以用来解决相应的推理问题。     

Special Cases and Substitutes for Rigid E-Unification

The simultaneous rigid E-unification problem arises naturally in theorem proving with equality. This problem has recently been shown to be undecidable. This raises the question whether simultaneous rigid E-unification can usefully be applied to equality theorem proving. We give some evidence in the affirmative, by presenting a number of common special cases in which a decidable version of this problem suffices for theorem proving with equality. We also present some general decidable methods of a rigid nature that can be used for equality theorem proving and discuss their complexity. Finally, we give a new proof of undecidability of simultaneous rigid E-unification which is based on Post's Correspondence Problem, and has the interesting feature that all the positive equations used are ground equations (that is, contain no variables). Received: March 6, 1997; revised version: August 13, 1999     

悖论逻辑的表演算

悖论逻辑ＬＰ是一个超协调逻辑，发展超协调逻辑（ＬＰ）的目的是使得不会从矛盾推出任一命题，但它有一个主要缺点：就是一些在经典逻辑中有效的推理在ＬＰ中不再有效；极小悖论逻辑ＬＰｍ能克服这个缺点，使得在没有矛盾的直接影响下超协调逻辑等价于经典逻辑．ＬＰ和ＬＰｍ原来都只给出语义定义，虽然已有ＬＰ的证明论，但如何得到一个ＬＰｍ的证明论仍是一个未解问题．本文提出了一种可靠与完全的表演算作为ＬＰ与ＬＰｍ的证明论．     

Dual Systems of Tableaux and Sequents for PLTL

On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph that must be checked and (possibly) pruned in a second phase of the refutation procedure. On the other hand, traditional sequent calculi for TL make use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automatization. A remarkable consequence of using auxiliary graphs in the tableaux framework and invariants or infinitary rules in the sequents framework is that TL fails to carry out the classical correspondence between tableaux and sequents. In this paper, we first provide a tableau method TTM that does not require auxiliary graphs to decide whether a set of PLTL-formulas is satisfiable. This tableau method TTM is directly associated to a one-sided sequent calculus called TTC. Since TTM is free from all the structural rules that hinder the mechanization of deduction, e.g. weakening and contraction, then the resulting sequent calculus TTC is also free from this kind of structural rules. In particular, TTC is free of any kind of cut, including invariant-based cut. From the deduction system TTC, we obtain a two-sided sequent calculus GTC that preserves all these good freeness properties and is finitary, sound and complete for PTL. Therefore, we show that the classical correspondence between tableaux and sequent calculi can be extended to TL. Every deduction system is proved to be complete. In addition, we provide illustrative examples of deductions in the different systems.     

Tableau Systems for Paraconsistency and Minimal Inconsistency

In this paper,the semantics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first.And then signed tableaux for paraconsistent logic and minimal tableaux for logic of minimal inconsistency is proposed.Finally,the reduction of logic of paraconsistency and minimal inconsistncy on ordinary semantics which provides new approach to proof procedure and implementation of paraconsistency and minimal inconsistency are provided.