21,439 research outputs found
On Generalized Dislocated Quasi Metrics
The notion of dislocated quasi metric is a generalization of metric that retains, an analogue of the illustrious Banach's Contraction principle and has useful applications in the semantic analysis of logic programming. In this paper we introduce the concept of generalized dislocated quasi metric space.The purpose of this note is to study topological properties of a metric, its connection with generalized dislocated metric space and to derive some fixed point theorems. Keywords: Generalized dislocated metric, Generalized dislocated quasi metric, Contractive conditions, coincidence point, b-property
Proof Outlines as Proof Certificates: A System Description
We apply the foundational proof certificate (FPC) framework to the problem of
designing high-level outlines of proofs. The FPC framework provides a means to
formally define and check a wide range of proof evidence. A focused proof
system is central to this framework and such a proof system provides an
interesting approach to proof reconstruction during the process of proof
checking (relying on an underlying logic programming implementation). Here, we
illustrate how the FPC framework can be used to design proof outlines and then
to exploit proof checkers as a means for expanding outlines into fully detailed
proofs. In order to validate this approach to proof outlines, we have built the
ACheck system that allows us to take a sequence of theorems and apply the proof
outline "do the obvious induction and close the proof using previously proved
lemmas".Comment: In Proceedings WoF'15, arXiv:1511.0252
A framework for proof certificates in finite state exploration
Model checkers use automated state exploration in order to prove various
properties such as reachability, non-reachability, and bisimulation over state
transition systems. While model checkers have proved valuable for locating
errors in computer models and specifications, they can also be used to prove
properties that might be consumed by other computational logic systems, such as
theorem provers. In such a situation, a prover must be able to trust that the
model checker is correct. Instead of attempting to prove the correctness of a
model checker, we ask that it outputs its "proof evidence" as a formally
defined document--a proof certificate--and that this document is checked by a
trusted proof checker. We describe a framework for defining and checking proof
certificates for a range of model checking problems. The core of this framework
is a (focused) proof system that is augmented with premises that involve "clerk
and expert" predicates. This framework is designed so that soundness can be
guaranteed independently of any concerns for the correctness of the clerk and
expert specifications. To illustrate the flexibility of this framework, we
define and formally check proof certificates for reachability and
non-reachability in graphs, as well as bisimulation and non-bisimulation for
labeled transition systems. Finally, we describe briefly a reference checker
that we have implemented for this framework.Comment: In Proceedings PxTP 2015, arXiv:1507.0837
Dual-Context Calculi for Modal Logic
We present natural deduction systems and associated modal lambda calculi for
the necessity fragments of the normal modal logics K, T, K4, GL and S4. These
systems are in the dual-context style: they feature two distinct zones of
assumptions, one of which can be thought as modal, and the other as
intuitionistic. We show that these calculi have their roots in in sequent
calculi. We then investigate their metatheory, equip them with a confluent and
strongly normalizing notion of reduction, and show that they coincide with the
usual Hilbert systems up to provability. Finally, we investigate a categorical
semantics which interprets the modality as a product-preserving functor.Comment: Full version of article previously presented at LICS 2017 (see
arXiv:1602.04860v4 or doi: 10.1109/LICS.2017.8005089
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