First-Order Transitive Closure Axiomatization via Iterative Invariant Injections
نویسندگان
چکیده
ion Rules Abst1: Variable instantiations with essential ground terms of complexity r (using a modified version of our work [SMT’2013]) Abst2: φ := (l ∨ φrest), (¬l ∨ Crest) ∈ CNF (F ) =⇒ φ φ[Crest / l ] Abst3: φ := (¬φ(t) ∨ φrest), t := pg =⇒ φ φ[(∀x . x = t ∨ (t, x)d ∈ tcR → φ(x)) / φ(t)]
منابع مشابه
Quantified Invariant Generation Using an Interpolating Saturation Prover
Interpolating provers have a variety of applications in verification, including invariant generation and abstraction refinement. Here, we extended these methods to produce universally quantified interpolants and invariants, allowing the verification of programs manipulating arrays and heap data structures. We show how a paramodulation-based saturation prover, such as SPASS, can be modified in a...
متن کاملConstructive Completeness for Modal Logic with Transitive Closure
Classical modal logic with transitive closure appears as a subsystem of logics used for program verification. The logic can be axiomatized with a Hilbert system. In this paper we develop a constructive completeness proof for the axiomatization using Coq with Ssreflect. The proof is based on a novel analytic Gentzen system, which yields a certifying decision procedure that for a formula construc...
متن کاملThe Definition of Transitive Closure with OCL
The Object Constraint Language (OCL) is based on firstorder logic and set theory. As the most well-known application, OCL is used to formulate well-formedness rules in the UML metamodel. Here, the transitive closure of a relationship is defined in terms of an OCL invariant, which seems to contradict classical results on the expressive power of first-order logic. In this paper, we give sufficien...
متن کاملTangled Modal Logic for Spatial Reasoning
We consider an extension of the propositional modal logic S4 which allows ♦ to act not only on isolated formulas, but also on sets of formulas. The interpretation of ♦Γ is then given by the tangled closure of the valuations of formulas in Γ, which over finite transitive, reflexive models indicates the existence of a cluster satisfying Γ. This extension has been shown to be more expressive than ...
متن کاملAutomata with Nested Pebbles Capture First-Order Logic with Transitive Closure
String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure h...
متن کامل