Related papers: Propositional Logics for the Lawvere Quantale
We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as preorders. The logic is equipped with a precise syntactic…
MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
I explore the relationships between Prawitz's approach to non-monotonic proof-theoretic validity, which I call reducibility semantics, and some later proof-theoretic approaches, which I call standard base semantics and Sandqvist's base…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
We consider the equivalence of Lawvere theories and finitary monads on Set from the perspective of Endf(Set)-enriched category theory, where Endf(Set) is the category of finitary endofunctors of Set. We identify finitary monads with…
In this paper, we present an abstract framework of many-valued modal logic with the interpretation of atomic propositions and modal operators as predicate lifting over coalgebras for an endofunctor on the category of sets. It generalizes…
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
Following Lawvere's description of metric spaces using enriched category theory, we introduce a change in the base of enrichment that allows description of some aspects of (relativistic) causal spaces. All such spaces are Cauchy complete,…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions…