Related papers: Topological Modal Logics with Difference Modality
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
The introduction of the categorical notion of closure operators has unified various important notions and has led to interesting examples and applications in diverse areas of mathematics (see for example, Dikranjan and Tholen (\cite{DT})).…
In 1997 Timothy J. Surendonk proved via algebraic semantics that all modal logics without iterative axioms are canonical and so strongly complete. In this paper, we continue the work done by Surendonk in this field. We use neighborhood…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
We present the set of axioms for topological space with the operation of boundary as primitive notion.
The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…
We explore an inquisitive modal logic designed to reason about neighborhood models. This logic is based on an inquisitive strict conditional operator, which quantifies over neighborhoods, and which can be applied to both statements and…
We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…
Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general…
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
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…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…