Related papers: First-Order Logical Duality
The paper studies computability-theoretic aspects of topological $T_0$-spaces. We introduce effective versions of the notions of a countable $c$-poset and a (second-countable) topological space with base. Based on this, we prove an…
Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
In this thesis we propose and study a theory of ordered locales, a type of point-free space equipped with a preorder structure on its frame of opens. It is proved that the Stone-type duality between topological spaces and locales lifts to a…
In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which…
We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in the full first-order model theory with negation…
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…
In this note we shall generalize the Stone duality between compact totally disconnected spaces and Boolean algebras to a duality between all complete non-Archimedean uniform spaces and Boolean algebras.
We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…
The aim of the present paper is to extend the dualizing object approach to Stone duality to the non-commutative setting of skew Boolean algebras. This continues the study of non-commutative generalizations of different forms of Stone…
Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…
Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…