Related papers: An Algebraic Semantics for Possibilistic Logic
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
One of the greatest problems in philosophy is that of meaning. The turning point in thinking on meaning was Tarski's definition of truth, and the rapid development of logical semantics and model theory was a consequence of this achievement.…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
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…
By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…
We propose a multi-agent epistemic logic capturing reasoning with degrees of plausibility that agents can assign to a given statement, with $1$ interpreted as "entirely plausible for the agent" and $0$ as "completely implausible" (i.e., the…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…