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Interpolation is an important component of recent methods for program verification. It provides a natural and effective means for computing separation between the sets of ‘good’ and ‘bad’ states. The existing algorithms for interpolant generation are proof-based: They require explicit construction of proofs, from which interpolants can be computed.… (More)
We show that for special types of extensions of a base theory, which we call local, efficient hierarchic reasoning is possible. We identify situations in which it is possible, for an extension T1 of a theory T0, to express the decidability and complexity of the universal theory of T1 in terms of the decidability resp. complexity of suitable fragments of the… (More)
The paper presents a modular superposition calculus for the combination of firstorder theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure – only involving clauses over the alphabet of either one, but not both, of the theories – when refuting goals represented by… (More)
In this paper we study interpolation in local extensions of a base theory. We<lb>identify situations in which it is possible to obtain interpolants in a hierarchical manner,<lb>by using a prover and a procedure for generating interpolants in the base theory as black-<lb>boxes. We present several examples of theory extensions in which interpolants can… (More)
We present a general framework which allows to identify complex theories important in verification for which efficient reasoning methods exist. The framework we present is based on a general notion of locality. We show that locality considerations allow us to obtain parameterized decidability and complexity results for many (combinations of) theories… (More)
We study possibilities of reasoning about extensions of base theories with functions which satisfy certain recursion (or homomorphism) properties. Our focus is on emphasizing possibilities of hierarchical and modular reasoning in such extensions and combinations thereof. We present practical applications in verification and cryptography.
We give a uniform method for automated reasoning in several types of extensions of ordered algebraic structures (definitional extensions, extensions with boundedness axioms or with monotonicity axioms). We show that such extensions are local and, hence, efficient methods for hierarchical reasoning exist in all these cases.
This system description provides an overview of H-PILoT (Hierarchical Proving by Instantiation in Local Theory extensions), a program for hierarchical reasoning in extensions of logical theories with functions axiomatized by a set of clauses. H-PILoT reduces deduction problems in the theory extension to deduction problems in the base theory. Specialized… (More)
In this paper we show that subsumption problems in many lightweight description logics (including EL and EL+) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras, to obtain uniform PTIME decision procedures for CBox subsumption in EL and… (More)