Related papers: Proof Theory for Bimodal Provability Logics

In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.

We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The…

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…

In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space…

This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion…

Using polyadic MV algebras, we show that many predicate many valued logics have the interpolation property.

This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…

Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…

This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation. We focus on showing…

Recent research has established complexity results for the problem of deciding the existence of interpolants in logics lacking the Craig Interpolation Property (CIP). The proof techniques developed so far are non-constructive, and no…

Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionistic basis through single-succedent sequent calculi. We adapt…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

The notion of linear exponential comonads on symmetric monoidal categories has been used for modelling the exponential modality of linear logic. In this paper we introduce linear exponential comonads on general (possibly non-symmetric)…

We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…

Following G. Mints(Kluwer 2000 and draft 2013), we present terminating and bicomplete proof searches in multi-succedent sequent calculi for intuitionistic propositional logic, fragments of intuitionistic predicate logic and full…

The goal of this paper is to establish that it remains undecidable whether a sequent is provable in two systems in which a weakening rule for an exponential modality is completely omitted from classical propositional linear logic…

We develop foundations for computing Craig interpolants and similar intermediates of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient…

The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…