Related papers: Interpolation in Non-Classical Logics
Interpolation-based techniques have become popularized in recent years because of their inherently modular and local reasoning, which can scale up existing formal verification techniques like theorem proving, model-checking, abstraction…
A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…
We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest…
The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that…
Craig's Interpolation theorem has a wide range of applications, from mathematical logic to computer science. Proof-theoretic techniques for establishing interpolation usually follow a method first introduced by Maehara for the Sequent…
We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic $\mathbf{IL}$. We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed…
Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…
We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable…
In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.
A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
We treat interpolation for various logics.
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
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…
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…
This paper is a historical tour of occurrences of the Craig interpolation theorem and the Beth definability theorem in philosophy since the 1950s. We identify the notion of dependence as one major red thread behind these, and include some…
Interpolation-based techniques become popular in recent years, as they can improve the scalability of existing verification techniques due to their inherent modularity and local reasoning capabilities. Synthesizing Craig interpolants is the…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…