Related papers: An Efficient Cyclic Entailment Procedure in a Frag…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Separation logic is successful for software verification in both theory and practice. Decision procedure for symbolic heaps is one of the key issues. This paper proposes a cyclic proof system for symbolic heaps with general form of…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
We develop a doubly-exponential decision procedure for the satisfiability problem of guarded separation logic -- a novel fragment of separation logic featuring user-supplied inductive predicates, Boolean connectives, and separating…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
Checking the soundness of cyclic induction reasoning for first-order logic with inductive definitions (FOLID) is decidable but the standard checking method is based on an exponential complement operation for B\"uchi automata. Recently, we…
Cyclic pre-proofs can be represented as sets of finite tree derivations with back-links. In the frame of the first-order logic with inductive definitions, the nodes of the tree derivations are labelled by sequents and the back-links connect…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on…
Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain…
A cyclic proof system generalises the standard notion of a proof as a finite tree of locally sound inferences by allowing proof objects to be potentially infinite. Regular infinite proofs can be finitely represented as graphs. To preclude…
The framework of cyclic proof systems provides a reasonable proof system for logics with inductive definitions. It also offers an effective automated proof search procedure for such logics without finding induction hypotheses. Recent…
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…