Related papers: Cyclic Negations and Four-valuedness
Bilingual machine-readable dictionaries are knowledge resources useful in many automatic tasks. However, compared to monolingual computational lexicons like WordNet, bilingual dictionaries typically provide a lower amount of structured…
In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While…
The logical connectives typically found in programming languages are similar to their mathematical counterparts, yet different due to their short-circuit behaviour -- when evaluating them, the second argument is only evaluated if the first…
Two possible realizations of the formal neuron are considered as quantum system. The first type complies with classical system. The second type vastly increases the possible problems.
The operad of moulds is realized in terms of an operational calculus of formal integrals (continuous formal power series). This leads to many simplifications and to the discovery of various suboperads. In particular, we prove a conjecture…
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always…
This piece threads substructurality and modality into a negation that activates the downside of equivalence and identity in a fibrational framework. The piece is a working through of negation and contradiction as type-theoretic/categorial…
The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…
Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a…
We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the…
We consider two expansions of G\"{o}del logic $\mathsf{G}$ with two versions of paraconsistent negation. The first one is $\mathsf{G_{inv}}$ -- the expansion of $\mathsf{G}$ with an involuitive negation ${\sim_\mathsf{i}}$ defined via…
In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra…