We show that the validity of Parikh's theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of μ-term equations of continuous commutative idempotent semirings.
The Liar paradox, or the sentenceI am now saying is falseits various guises have been attracting the attention of logicians and linguists since ancient times. A commonly accepted treatment of the Liar paradox [7,8] is by means of Situation semantics, a powerful approach to natural language analysis. It is based on the machinery of non-well-founded sets developed in [1]. In this paper we show how to generalize these results including elements of fuzzy and intuitionistic fuzzy logic [3,4]. Basing...
In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are...
This paper deals with the use of fuzzy set theory as a viable alternative method for modelling and solving the stochastic assembly line balancing problem. Variability and uncertainty in the assembly line balancing problem has traditionally been modelled through the use of statistical distributions. This may not be feasible in cases where no historical data exists. Fuzzy set theory allows for the consideration of the ambiguity involved in assigning processing and cycle times and the uncertainty contained...
The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed ω-semigroups of width 2 and height ωω. This paper completes the description of this algebraic hierarchy. We first give a purely algebraic decidability procedure of this partial ordering by introducing a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of any ω-rational language can therefore be computed...
The algebraic study of formal languages shows that ω-rational sets correspond precisely to the ω-languages recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on...
We develop a calculus for the oscillation index of Baire one functions using gauges analogous to the modulus of continuity.
We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and -additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.
In this paper we present a very general deduction theorem which -based upon a uniform notion of proof from hypotheses- holds for a very large class of logical systems. Most of the known results for classical and modal logics, as well as new results, are immediate corollaries of this theorem.