Related papers: Fredkin Gates for Finite-valued Reversible and Con…
Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary…
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish…
This paper is devoted to the construction of conditional logic system of {\L}ukasiewicz m-valued propositional logic. We construct conditional logic system {\L}CR based on {\L}ukasiewicz m-valued propositional logic. We construct world…
We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal…
We investigate some well-known (and a few not-so-well-known) many-valued logics that have a small number (3 or 4) of truth values. For some of them we complain that they do not have any \emph{logical} use (despite their perhaps having some…
We introduce a new propositional logic, called very weak subintuitionistic logic $\mathbf{VF}$, by adapting the relational semantics of Fitting, Marek, and Truszczy\'nski for the pure logic of necessitation $\mathbf{N}$ to the propositional…
Weak Kleene logics are three-valued logics characterized by the presence of an infectious truth-value. In their external versions, as they were originally introduced by Bochvar and Hallden, these systems are equipped with an additional…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
We study a many-valued generalization of Propositional Dynamic Logic where formulas in states and accessibility relations between states of a Kripke model are evaluated in a finite FL-algebra. One natural interpretation of this framework is…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
In this report reversible Toffoli and quantum Deutsch gates are extended to the p_valued domain. Their structural parameters are determined and their behavior is proven. Both conjunctive and disjunctive control strategies with positive and…
We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding…
Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk,…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Glivenko's theorem says that, in propositional logic, classical provability of a formula entails intuitionistic provability of double negation of that formula. We generalise Glivenko's theorem from double negation to an arbitrary nucleus,…
In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
Continuing to pursue a research direction that we already explored in connection with G\"odel-Dummett logic and Ruspini partitions, we show here that {\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy…
Involutive Stone algebras (or {\bf S}--algebras) were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued \L ukasiewicz--Moisil algebras. In this work we focus on the logic that preserves degrees of truth…