In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P. -D. Février’s ’logic of complementarity’ as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is...

In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap’s four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap’s logic. Like truth-values of Belnap’s logic, relative sets have two orderings; one is an order of inclu...

We present a new approach for finding generalized contingent plans with loops and branches in situations where there is uncertainty in state properties and object quantities, but lack of probabilistic information about these uncertainties. We use a state abstraction technique from static analysis of programs, which uses 3-valued logic to compactly represent belief states with unbounded numbers ...

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Motivated by Wilmshurst’s conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach which is a combination of two methods from numerical algebraic geometry: numerical polynomial homotopy continuation to compute a numerical approximation of each zero and Smale’s alpha-theory to certify the results. Using this approach, we provide new examples of harmo...

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NULL is a special marker used in SQL to indicate that a value for an attribute of an object does not exist in the database. Its aim is a representation of “missing information and inapplicable information”. Although NULL is called null ‘value’ is not at all a value. It is a marker. It is only an annotation of incomplete data. Since it is typically interpreted as a value, NULL has led to controv...

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.

Choices in business processes are often based on the process history saved as a log-file listing events and their time stamps. In this paper we introduce a finite-path variant of the timed propositional logics with past for specifying guards in business process models. The novelty is due to the introduction of boundary points start and now corresponding to the starting and current observation p...

The paper investigates the characterisation of vague concepts within the framework of modal logic. This work builds on the su-pervaluation approach of Fine and exploits the idea of a precisiication space. A simple language is presented with two modalities: a necessity operator and an operatorìt is unequivocal that' which is used to articulate the logic of vagueness. Both these operators obey th...