Explore the vast range of titles available.

In this paper, we shall give another proof of the faithfulness of Blass translation (for short, B-translation) of the propositional fragment L₁ of Leśniewski's ontology in the modal logic K by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic PrL (= GL), that is, K + □(□φ ⊃ φ) ⊃ □φ. The faithfulness also holds for normal modal logics, e.g., KD, K4, KD4, KB. We shall conclude this paper with the section of some open problems and conjectures.

In this paper, we prove the semantic incompleteness of some expansions of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that were proposed in Liberman et al. (2020) “Dynamic Term-modal Logics for First-order Epistemic Planning.” Term-modal logic is a family of first-order modal logics having term-modal operators indexed with terms in the first-order language. While some first-order formula is valid over the corresponding class of frames in the involved Kripke semantics, it is not provable in those expansions. We show this fact by introducing a non-standard Kripke semantics which makes the meanings of constants and function symbols relative to the meanings of relation symbols combined with them. We also address an incorrect frame correspondence result given in Liberman et al. (2020).

We study two kinds of combined modal logics, semiproducts and products with , and their connection with modal predicate logics. We present examples of propositional modal logics, for which semiproducts or products with are axiomatized in the minimal way (they are called semiproduct- or product-matching with ) and also present counterexamples for these properties. The finite model property for (semi)products, together with (semi)product-matching, allow us to obtain decidability of corresponding 1-variable modal predicate logics.

We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of ‘finite achronal width’ that are introduced here.

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of \"evidence management\", ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

This paper is a study of higher-order contingentism — the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations.

Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives ∧, ∨, □ and ◇· We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a (categorical) duality between so-called M⁺ -spaces (poset-based monotone neighbourhood frames with extra structure) and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.

In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\\varphi$ is not satisfied in a given world, but we still believe in it (or we think that it should be accepted). Another interpretations are also possible: e.g. that we do not accept $\\varphi$ but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is expressed by an adequate form of modal operator $\\mathsf{W}$ which is interpreted in relational frames with neighborhoods. We discuss monotonicity of forcing, soundness, completeness and several other issues. Finally, we mention the fact that it is possible to investigate intuitionistic logics of unknown truths.

Building theories of organizations is challenging: theories are partial and \"folk\" categories are fuzzy. The commonly used tools--first-order logic and its foundational set theory--are ill-suited for handling these complications. Here, three leading authorities rethink organization theory. Logics of Organization Theory sets forth and applies a new language for theory building based on a nonmonotonic logic and fuzzy set theory. In doing so, not only does it mark a major advance in organizational theory, but it also draws lessons for theory building elsewhere in the social sciences.

In this paper, we shall show that the following translation IM from the propositional fragment L1 of Leśniewski's ontology to modal logic KTB is sound: for any formula ϕ and ψ of L1, it is defined as(M1) IM(ϕ∨ψ)=IM(ϕ)∨IM(ψ),(M2) IM(¬ϕ)=¬IM(ϕ),(M3) IM(ϵab)=◊pa⊃pa.∧.◻pa⊃◻pb.∧.◊pb⊃pa,where pa and pb are propositional variables corresponding to the name variables a and b, respectively. In the last, we shall give some comments including some open problems and my conjectures.