Related papers: Circular Proofs for G\"odel-L\"ob Logic
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various…
A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Delta-complexes. The Euclidean and projective interpretations of the sequents are defined…
We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from algebraic logic to categorical logic.
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
Sandqvist gave a proof-theoretic semantics (P-tS) for classical logic (CL) that explicates the meaning of the connectives without assuming bivalance. Later, he gave a semantics for intuitionistic propositional logic (IPL). While soundness…
In this work we investigate the chordality of squares and line graph squares of graphs. We prove a sufficient condition for the chordality of squares of graphs not containing induced cycles of length at least five. Moreover, we characterize…
This paper introduces a class of linear programming examples which cause the simplex method to cycle indefinitely and which are the simplest possible examples showing this behaviour. The structure of examples from this class repeats after…
We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…
The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…
Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
In this paper we present a new proof of Solovay's theorem on arithmetical completeness of G\"odel-L\"ob provability logic GL. Originally, completeness of GL with respect to interpretation of $\Box$ as provability in PA was proved by R.…
In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…