Related papers: Algebraic Semantics for Relative Truth, Awareness,…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Dialectical frameworks are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. Their generality allow them to cover a number of…
Applying logic in the area of conceptual modeling has been investigated widely, yet there has been limited uptake of logic-based conceptual modeling in industry. According to some researchers, another formalization of such tools as EER or…
The four-valued semantics of Belnap--Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several non-classical logics depending on which feature of propositions we wish to preserve: truth, non-falsity,…
Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master equations, which can be interpreted as…
In this paper we continue the investigation of a real number object, i.e., an object representing the real numbers, in categories of relations. Our axiomatization is based on a relation algebraic version of Tarski's axioms of the real…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
Coalgebra, as the abstract study of state-based systems, comes naturally equipped with a notion of behavioural equivalence that identifies states exhibiting the same behaviour. In many cases, however, this equivalence is finer than the…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency…
We investigate the orthoalgebras of certain non-Boolean models which have a classical realization. Our particular concern will be the partition logics arising from the investigation of the empirical propositional structure of Moore and…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of…
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…
Robots assisting humans in complex domains have to represent knowledge and reason at both the sensorimotor level and the social level. The architecture described in this paper couples the non-monotonic logical reasoning capabilities of a…
Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…