Related papers: Moving up and down in the generic multiverse
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of the geometric structure of symmetric…
We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models and, hence, the results apply to a wide class of modal logics including, for example,…
The possibility of fundamental theories with very many ground states, each with different physical parameters, changes the way that we approach the major questions of particle physics. Most importantly, it raises the possibility that these…
This paper is focused on the study of modal logics defined from valued Kripke frames, and particularly, on computability and expressibility questions of modal logics of transitive Kripke frames evaluated over certain residuated lattices. It…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
We have previously introduced role logic as a notation for describing properties of relational structures in shape analysis, databases and knowledge bases. A natural fragment of role logic corresponds to two-variable logic with counting and…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that…
Given a class $\mathcal C$ of models, a binary relation ${\mathcal R}$ between models, and a model-theoretic language $L$, we consider the modal logic and the modal algebra of the theory of $\mathcal C$ in $L$ where the modal operator is…
Human perception of the empirical world involves recognizing the diverse appearances, or 'modalities', of underlying objects. Despite the longstanding consideration of this perspective in philosophy and cognitive science, the study of…
The trajectories of a rational motion given by a polynomial of degree n in the dual quaternion model of rigid body displacements are generically of degree 2n. In this article we study those exceptional motions whose trajectory degree is…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is…
Standard models of multi-agent modal logic do not capture the fact that information is often \emph{ambiguous}, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different…