206 research outputs found
Automatically Verifying Temporal Properties of Pointer Programs with Cyclic Proof
In this article, we investigate the automated verification of temporal properties of heap-aware programs. We propose a deductive reasoning approach based on cyclic proof. Judgements in our proof system assert that a program has a certain temporal property over memory state assertions, written in separation logic with user-defined inductive predicates, while the proof rules of the system unfold temporal modalities and predicate definitions as well as symbolically executing programs. Cyclic proofs in our system are, as usual, finite proof graphs subject to a natural, decidable soundness condition, encoding a form of proof by infinite descent. We present a proof system tailored to proving CTL properties of nondeterministic pointer programs, and then adapt this system to handle fair execution conditions. We show both versions of the system to be sound, and provide an implementation of each in the Cyclist theorem prover, yielding an automated tool that is capable of automatically discovering proofs of (fair) temporal properties of pointer programs. Experimental evaluation of our tool indicates that our approach is viable, and offers an interesting alternative to traditional model checking techniques
Integrating a Global Induction Mechanism into a Sequent Calculus
Most interesting proofs in mathematics contain an inductive argument which
requires an extension of the LK-calculus to formalize. The most commonly used
calculi for induction contain a separate rule or axiom which reduces the valid
proof theoretic properties of the calculus. To the best of our knowledge, there
are no such calculi which allow cut-elimination to a normal form with the
subformula property, i.e. every formula occurring in the proof is a subformula
of the end sequent. Proof schemata are a variant of LK-proofs able to simulate
induction by linking proofs together. There exists a schematic normal form
which has comparable proof theoretic behaviour to normal forms with the
subformula property. However, a calculus for the construction of proof schemata
does not exist. In this paper, we introduce a calculus for proof schemata and
prove soundness and completeness with respect to a fragment of the inductive
arguments formalizable in Peano arithmetic.Comment: 16 page
Cyclic abduction of inductively defined safety and termination preconditions
We introduce cyclic abduction: a new method for automatically inferring safety and termination preconditions of heap manipulating while programs, expressed as inductive definitions in separation logic. Cyclic abduction essentially works by searching for a cyclic proof of the desired property, abducing definitional clauses of the precondition as necessary in order to advance the proof search process.
We provide an implementation, Caber, of our cyclic abduction method, based on a suite of heuristically guided tactics. It is often able to automatically infer preconditions describing lists, trees, cyclic and composite structures which, in other tools, previously had to be supplied by hand
The Lambek calculus with iteration: two variants
Formulae of the Lambek calculus are constructed using three binary
connectives, multiplication and two divisions. We extend it using a unary
connective, positive Kleene iteration. For this new operation, following its
natural interpretation, we present two lines of calculi. The first one is a
fragment of infinitary action logic and includes an omega-rule for introducing
iteration to the antecedent. We also consider a version with infinite (but
finitely branching) derivations and prove equivalence of these two versions. In
Kleene algebras, this line of calculi corresponds to the *-continuous case. For
the second line, we restrict our infinite derivations to cyclic (regular) ones.
We show that this system is equivalent to a variant of action logic that
corresponds to general residuated Kleene algebras, not necessarily
*-continuous. Finally, we show that, in contrast with the case without division
operations (considered by Kozen), the first system is strictly stronger than
the second one. To prove this, we use a complexity argument. Namely, we show,
using methods of Buszkowski and Palka, that the first system is -hard,
and therefore is not recursively enumerable and cannot be described by a
calculus with finite derivations
A Decision Procedure for String Logic with Quadratic Equations, Regular Expressions and Length Constraints
A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic
We define a infinitary labelled sequent calculus for PDL, G3PDL^{\infty}. A
finitarily representable cyclic system, G3PDL^{\omega}, is then given. We show
that both are sound and complete with respect to standard models of PDL and,
further, that G3PDL^{\infty} is cut-free complete. We additionally investigate
proof-search strategies in the cyclic system for the fragment of PDL without
tests
Optimal functional outcome measures for assessing treatment for Dupuytren's disease: A systematic review and recommendations for future practice
This article is available through the Brunel Open Access Publishing Fund. Copyright © 2013 Ball et al.; licensee BioMed Central Ltd.Background: Dupuytren's disease of the hand is a common condition affecting the palmar fascia, resulting in progressive flexion deformities of the digits and hence limitation of hand function. The optimal treatment remains unclear as outcomes studies have used a variety of measures for assessment. Methods: A literature search was performed for all publications describing surgical treatment, percutaneous needle aponeurotomy or collagenase injection for primary or recurrent Dupuytren’s disease where outcomes had been monitored using functional measures. Results: Ninety-one studies met the inclusion criteria. Twenty-two studies reported outcomes using patient reported outcome measures (PROMs) ranging from validated questionnaires to self-reported measures for return to work and self-rated disability. The Disability of Arm, Shoulder and Hand (DASH) score was the most utilised patient-reported function measure (n=11). Patient satisfaction was reported by eighteen studies but no single method was used consistently. Range of movement was the most frequent physical measure and was reported in all 91 studies. However, the methods of measurement and reporting varied, with seventeen different techniques being used. Other physical measures included grip and pinch strength and sensibility, again with variations in measurement protocols. The mean follow-up time ranged from 2 weeks to 17 years. Conclusions: There is little consistency in the reporting of outcomes for interventions in patients with Dupuytren’s disease, making it impossible to compare the efficacy of different treatment modalities. Although there are limitations to the existing generic patient reported outcomes measures, a combination of these together with a disease-specific questionnaire, and physical measures of active and passive individual joint Range of movement (ROM), grip and sensibility using standardised protocols should be used for future outcomes studies. As Dupuytren’s disease tends to recur following treatment as well as extend to involve other areas of the hand, follow-up times should be standardised and designed to capture both short and long term outcomes
Febrile patients admitted to remote hospitals in Northeastern Kenya: seroprevalence, risk factors and a clinical prediction tool for Q-Fever
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