Related papers: A logic of co-valuations
We introduce Value Coalition Logic, a typed assignment-based reconstruction of classical coalition logic. The strategic semantics is unchanged: coalitional ability is still interpreted by the standard one-step game-form clause. The change…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
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…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…
Cobordism categories are known to be compact closed. They can therefore be used to define non-degenerate models of multiplicative linear logic by combining the Int construction with double glueing. In this work we detail such construction…
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…