Related papers: Negative Translations for Affine and Lukasiewicz L…
We study a real valued propositional logic with unbounded positive and negative truth values that we call R-valued logic. Such logic slightly extends continuous propositional logic which, in turn, builds on Lukasiewicz many-valued logic.…
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization…
It is well-known that the functions $f \in L^1(\mathbb{R}^d)$ whose translates along a lattice $\Lambda$ form a tiling, can be completely characterized in terms of the zero set of their Fourier transform. We construct an example of a…
The discussion about how to put together Gentzen's systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called Ecumenical Systems,…
In this paper, we show our results on the bi-directional data exchange between the F-logic language supported by the Flora2 system and the OWL language. Most of the TBox and ABox axioms are translated preserving the semantics between the…
From the viewpoint of provability, we compare some Gentzen-type hypersequent calculi for first-order infinite-valued {\L}ukasiewicz logic and for first-order rational Pavelka logic with each other and with H\'ajek's Hilbert-type calculi for…
In this paper, we provide a complete classification for the first-order Goedel logics concerning the property that the formulas admit logically equivalent prenex normal forms. We show that the only first-order Goedel logics that admit such…
We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…
In this paper we study intermediate logics between the degree preserving companion of Godel fuzzy logic with an involution and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts.…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
In this note we prove that single-conclusion admissible rules of any proper axiomatic extension of the infnite valued Lukasiewicz logic are finitely based.
In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, exhibiting a classical…
We consider a many-sorted variant of Japaridze's polymodal provability logic $\mathsf{GLP}$. In this variant, which is denoted $\mathsf{GLP}^\ast$, propositional variables are assigned sorts $\alpha \leq \omega$, where variables of finite…
In 1933, G\"odel introduced a provability interpretation of the propositional intuitionistic logic to establish a formalization for the BHK interpretation. He used the modal system, $\mathbf{S4}$, as a formalization of the intuitive concept…
Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…
Coven and Meyerowitz formulated two conditions which have since been conjectured to characterize all finite sets that tile the integers by translation. By periodicity, this conjecture is reduced to sets which tile a finite cyclic group…
Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular…
The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules…
Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general,…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…