Related papers: From Interpolating Formulas to Separating Language…
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…
Craig interpolation is used in program verification for automating key tasks such as the inference of loop invariants and the computation of program abstractions. This chapter covers some of the most important techniques that have been…
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…
The increasing popularity of automated tools for software and hardware verification puts ever increasing demands on the underlying decision procedures. This paper presents a framework for distributed decision procedures (for first-order…
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…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…
None of the first-order modal logics between $\mathsf{K}$ and $\mathsf{S5}$ under the constant domain semantics enjoys Craig interpolation or projective Beth definability, even in the language restricted to a single individual variable. It…
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…
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…
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 develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems…
In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant…
The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for…
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.
Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the…
Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig…
In this article, a model-theoretic approach is proposed to prove that the first-order G\"odel logic, $\mathbf{G}$, as well as its extension $\mathbf{G}^\Delta$ associated with first-order relational languages enjoy the Craig interpolation…
In this chapter, we present six different proofs of Craig interpolation for the modal logic K, each using a different set of techniques (model-theoretic, proof-theoretic, syntactic, automata-theoretic, using quasi-models, and algebraic). We…
We study the Lyndon interpolation property (LIP) and the uniform Lyndon interpolation property (ULIP) for extensions of $\mathbf{S4}$ and intermediate propositional logics. We prove that among the 18 consistent normal modal logics of finite…