We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize t...

This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems. A Belief Maintenance System hal! been constructed which manages a current set of probabilistic beliefs in much the same way that a TMS manages a set of true/false beliefs. Such a system may be thought of as a generalization of a. Truth Maintenance System. It enables one to reason using normal...

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...

This paper looks at logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.

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...

We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for buffer content process in vector-valued Skorokhod space which is endowed product $$J_1$$ topology. To illustrate our framework, we provide explicit tandem queue. At heart proof recent sample-path result, and nov...

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...

Understanding how deep learning architectures work is a central scientific problem. Recently, correspondence between neural networks (NNs) and Euclidean quantum field theories (QFTs) has been proposed. This investigates this in the framework of p-adic statistical (SFTs) (NNs). In case, fields are real-valued functions defined on an infinite regular rooted tree with valence p, fixed prime number...