3,714 research outputs found
Equivalence in QCSP (QBF)
The QBF validity problem with any propositional formulamay be seen as a QCSP. In this frame, we introduce a new constraint: the equivalence constraint and prove that it is stronger than equality constraint. In order to design this equivalence constraint, we introduce a new sequent calculus for QBF which is based on an equivalence relation over subformulae. This sequent calculus is proven to be sound and complete w.r.t. the semantics of the QBF. Based on this system, we define our equivalence constraint in such a way that QCSP(QBF) may be seen as a CSP(QBF) with a quantied search algorithm. We report some experiments in a generic constraint development environment
A Labelled Sequent Calculus for BBI: Proof Theory and Proof Search
We present a labelled sequent calculus for Boolean BI, a classical variant of
O'Hearn and Pym's logic of Bunched Implication. The calculus is simple, sound,
complete, and enjoys cut-elimination. We show that all the structural rules in
our proof system, including those rules that manipulate labels, can be
localised around applications of certain logical rules, thereby localising the
handling of these rules in proof search. Based on this, we demonstrate a free
variable calculus that deals with the structural rules lazily in a constraint
system. A heuristic method to solve the constraints is proposed in the end,
with some experimental results
A Hybrid Linear Logic for Constrained Transition Systems
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus
A Hybrid Linear Logic for Constrained Transition Systems with Applications to Molecular Biology
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus. We also present some preliminary experiments of direct encoding of biological systems in the logic
A simple sequent calculus for nominal logic
Nominal logic is a variant of first-order logic that provides support for
reasoning about bound names in abstract syntax. A key feature of nominal logic
is the new-quantifier, which quantifies over fresh names (names not appearing
in any values considered so far). Previous attempts have been made to develop
convenient rules for reasoning with the new-quantifier, but we argue that none
of these attempts is completely satisfactory.
In this article we develop a new sequent calculus for nominal logic in which
the rules for the new- quantifier are much simpler than in previous attempts.
We also prove several structural and metatheoretic properties, including
cut-elimination, consistency, and equivalence to Pitts' axiomatization of
nominal logic
A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems
Basic proof-search tactics in logic and type theory can be seen as the
root-first applications of rules in an appropriate sequent calculus, preferably
without the redundancies generated by permutation of rules. This paper
addresses the issues of defining such sequent calculi for Pure Type Systems
(PTS, which were originally presented in natural deduction style) and then
organizing their rules for effective proof-search. We introduce the idea of
Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the
syntax of a permutation-free sequent calculus for propositional logic due to
Herbelin, which is strongly related to natural deduction and already well
adapted to proof-search. The operational semantics is adapted from Herbelin's
and is defined by a system of local rewrite rules as in cut-elimination, using
explicit substitutions. We prove confluence for this system. Restricting our
attention to PTSC, a type system for the ground terms of this system, we obtain
the Subject Reduction property and show that each PTSC is logically equivalent
to its corresponding PTS, and the former is strongly normalising iff the latter
is. We show how to make the logical rules of PTSC into a syntax-directed system
PS for proof-search, by incorporating the conversion rules as in
syntax-directed presentations of the PTS rules for type-checking. Finally, we
consider how to use the explicitly scoped meta-variables of PTSCalpha to
represent partial proof-terms, and use them to analyse interactive proof
construction. This sets up a framework PE in which we are able to study
proof-search strategies, type inhabitant enumeration and (higher-order)
unification
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