Related papers: Ecumenical modal logic
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
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 previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
Fuzzy logic extends the classical truth values "true" and "false" with additional truth degrees in between. More specifically, fuzzy modal logics in this sense are given by a choice of fuzzy modalities and a fuzzy propositional base. It has…
We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett's and Dag Prawitz' philosophical motivations and…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…
This paper investigates the contingency of logic within the framework of possible world semantics. Possible world semantics captures the meaning of necessitation, i.e., a statement is necessarily true if it holds in all possible worlds.…
Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction. In the literature on proof-theoretic semantics, this principle is often coupled with another that is…
This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…
We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our…