Related papers: Splitting Proofs for Interpolation
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…
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…
In this chapter we give a basic overview of known results regarding Craig interpolation for first-order logic as well as for fragments of first-order logic. Our aim is to provide an entry point into the literature on interpolation theorems…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
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…
We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where…
Motivated by applications of first-order theorem proving to software analysis, we introduce a new inference rule, called subsumption demodulation, to improve support for reasoning with conditional equalities in superposition-based theorem…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the…
The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is…
Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal…
This paper is devoted to a new first order Taylor-like formula where the corresponding remainder is strongly reduced in comparison with the usual one which appears in the classical Taylor's formula. To derive this new formula, we introduce…
Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement.…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…
We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there are well-investigated trace-based…
Existing techniques for Craig interpolation for the quantifier-free fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning $(A, B)$ of the interpolation…
We generalize several propositional preprocessing techniques to higher-order logic, building on existing first-order generalizations. These techniques eliminate literals, clauses, or predicate symbols from the problem, with the aim of…