Related papers: Cyclic Negations and Four-valuedness
Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between $\textbf{mbCcl}$ and $\textbf{Cila}$. In order to overcome this limitation, we…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square $\{\pm 1\}$-matrices of size congruent to $2$ modulo $4$. Quasi-orthogonal cocycles are analogous to the orthogonal…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one…
We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of $\mathbb F_{p^n}\setminus…
The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a finite set, C be a finite cyclic group acting on X, and f(q) be a polynomial in q with nonnegative integer coefficients. Then the triple…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the…
We present a labelled and non-wellfounded calculus for the bimodal provability logic CS. The system is obtained by modelling the Kripke-like semantics of this logic. As in arXiv:2309.00532, we enforce the second-order property of converse…
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and…
We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…
We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible…
Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, L\"ob's formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings,…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…