Bilattices and d-frames are two different kinds of structures with a four-valued interpretation. Whereas d-frames were introduced with their topological semantics in mind, the theory of bilattices has a closer connection with logic. We consider a common generalisation of both structures and show that this not only still has a clear bitopological semantics, but that it also preserves most of the...

Sugeno integrals are a well-known family of qualitative multiple criteria aggregation operators. The paper investigates how the behavior of these operators can be described in a prioritized propositional logic language, namely possibilistic logic. The case of binary-valued criteria, which amounts to providing a logical description of the fuzzy measure underlying the integral, is first considere...

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...

We address the problem of computing and learning multivalued multithreshold perceptrons. Every ninput k-valued logic function can be implemented using a (k; s)-perceptron, for some number of thresholds s. We propose a genetic algorithm to search for an optimal (k; s)-perceptron that e ciently realizes a given multiple-valued logic function, that is to minimize the number of thresholds. Experime...

Signed formula can be used to reason about a wide variety of multiple-valued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in 26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint logic programming. Applications to bilattice logic programming and truth-maintenance are considered.

We study ultrafast operation of multiple-valued quantizers composed of resonant-tunneling diodes (RTDs) and high electron mobility transistors (HEMTs). The operation principle of these quantizers is based on the monostable-multistable transition logic (MML) of series-connected RTDs. The quantizers are fabricated by monolithically integrating InP-based RTDs and 0.7-μm-gate-length HEMTs with a cu...

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...

Multiple Valued Logic (MVL) has some important benefits such as increased data density, increased computational ability, reduced dynamic power dissipation Therefore with the help of Multiple Valued Logic (MVL) we have designed two quaternary multiplier architecture. The partial products in the multiplier are designed with quaternary voltage mode circuits. Each multiplier architecture is designe...

In this paper I propose the non-Archimedean multiple-validity. Further, I build an infinite-order predicate logical language in that predicates of various order are considered as fuzzy relations. Such a language can have non-Archimedean valued semantics. For instance, infinite-order predicates can have an interpretation in the set [0, 1] of hyperreal (hyperrational) numbers. Notice that there e...