Related papers: On the strongest three-valued paraconsistent logic…
We present a procedure which allows us to recover classical and nonclassical logical structures as \emph{concrete logics} associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for…
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.…
The thesis of this paper is that truth-relevant logic is a better foundation for mathematics than classical logic. It is a system proposed by Richard Diaz in 1981. In a certain sense t-relevant logic is based on Kleene strong tables. These…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
We say that a logic L has the Lyndon positivity property (LPP) if all formulas which are monotone in L (that is, are preserved under increasing the valuation on L-algebras) are L-equivalent to positive formulas (formulas without negation…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth \letf, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). \letf\ is an…
A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Ordinary first-order logic has the property that two formulas \phi and \psi have the same meaning in a structure if and only if the formula ``\phi iff \psi'' is true in the structure. We prove that independence-friendly logic does not have…
In this talk - based on the results of a forthcoming paper (Coletti, Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on "Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri, Italy, 2001) -…
A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…
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,…
A propositional logic program $P$ may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, describes…
The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent.…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
In this paper the 3-valued paraconsistent first-order logic QCiore is studied from the point of view of Model Theory. The semantics for QCiore is given by partial structures, which are first-order structures in which each n-ary predicate R…
We study rational functions over finite fields under PGL-equivalence. We say that $f, g \in \Bbb F_q(X)$ are \emph{equivalent} if there exist $\psi, \phi \in \Bbb F_q(X)$ of degree one such that $g = \psi \circ f \circ \phi$. Most…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…