The aim of this paper is to define the productoperation on a family of interval valued events and the notion ofjoint interval valued observable. We show the connection betweenproduct operations for interval valued events and intuitionisticfuzzy events, too. We display the relation between joint intervalvalued observable and joint intuitionistic fuzzy observable. We...

It is argued that the ‘inner’ negation ∼ familiar from 3-valued logic can be interpreted as a form of ‘conditional’ negation: ∼A is read “A is false if it has a truth value”. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language ...

Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional log...

The Poisson process is one of the most widely used models of a continuous time stochastic process. Along with Brownian motion, it can be considered as a fundamental example of such processes. The Poisson process is a counting process Nt, t ≥ 0, (a non-decreasing integer-valued process which counts the number of ‘points’ or ‘events’ up to time t) indexed by the time parameter t, which will be po...

While the purpose of conventional proof calculi is to axiomatise the set of valid sentences of a logic, refutation systems axiomatise the invalid sentences. Such systems are relevant not only for proof-theoretic reasons but also for realising deductive systems for nonmonotonic logics. We introduce Gentzen-type refutation systems for two basic three-valued logics and we discuss an application of...

To further increase the speed of computation, this paper aims to design and implement digital circuits entirely within the domain of multi-valued logic. In a fourvalued logic circuit, each wire carries two bits at a time, each logic gate operates two bits at once, and each memory cell records two bits at one time. To make the multi-valued computation possible, this paper describes a simple four...