Automated Reasoning in Quantified Modal and Temporal Logics

Centre for Intelligent Systems and their ApplicationsThis thesis is about automated reasoning in quantified modal and temporal logics, with an application to formal methods. Quantified modal and temporal logics are extensions of classical first-order logic in which the notion of truth is extended to take into account its necessity or equivalently, in the temporal setting, its persistence through time. Due to their high complexity, these logics are less widely known and studied than their propositional counterparts. Moreover, little so far is known about their mechanisability and usefulness for formal methods. The relevant contributions of this thesis are threefold: firstly, we devise a sound and complete set of sequent calculi for quantified modal logics; secondly, we extend the approach to the quantified temporal logic of linear, discrete time and develop a framework for doing automated reasoning via Proof Planning in it; thirdly, we show a set of experimental results obtained by applying the framework to the problem of Feature Interactions in telecommunication systems. These results indicate that (a) the problem can be concisely and effectively modeled in the aforementioned logic, (b) proof planning actually captures common structures in the related proofs, and (c) the approach is viable also from the point of view of efficiency

Fine-grained access control via policy-carrying data

W. W. Vasconcelos acknowledges the support of the Engineering and Physical Sciences Research Council (EPSRC, UK) within the research project “Scrutable Autonomous Systems” (SAsSY, http://www.scrutable-systems.org, Grant ref. EP/J012084/1). Also in: Journal ACM Transactions on Reconfigurable Technology and Systems (TRETS) - Special Section on FCCM 2016 and Regular Papers TRETS Homepage archive Volume 11 Issue 1, March 2018 Article No. 31 ACM New York, NY, USAPeer reviewedPostprin

A Proof Planning Framework For Isabelle

Centre for Intelligent Systems and their ApplicationsProof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully formal proofs. This thesis concerns the development and analysis of a novel approach to proof planning that focuses on an explicit representation of choices during search. We embody our approach as a proof planner for the generic proof assistant Isabelle and use the Isar language, which is human-readable and machine-checkable, to represent proof plans. Within this framework we develop an inductive theorem prover as a case study of our approach to proof planning. Our prover uses the difference reduction heuristic known as rippling to automate the step cases of the inductive proofs. The development of a flexible approach to rippling that supports its various modifications and extensions is the second major focus of this thesis. Here, our inductive theorem prover provides a context in which to evaluate rippling experimentally. This work results in an efficient and powerful inductive theorem prover for Isabelle as well as proposals for further improving the efficiency of rippling. We also draw observations in order to direct further work on proof planning. Overall, we aim to make it easier for mathematical techniques, and those specific to mechanical theorem proving, to be encoded and applied to problems

Automated reasoning in quantified modal and temporal logics

This thesis is about automated reasoning in quantified modal and temporal logics, with an application to formal methods. Quantified modal and temporal logics are extensions of classical first-order logic in which the notion of truth is extended to take into account its necessity or equivalently, in the temporal setting, its persistence through time. Due to their high complexity, these logics are less widely known and studied than their propositional counterparts. Moreover, little so far is known about their mechanisability and usefulness for formal methods. The relevant contributions of this thesis are threefold: firstly, we devise a sound and complete set of sequent calculi for quantified modal logics; secondly, we extend the approach to the quantified temporal logic of linear, discrete time and develop a framework for doing automated reasoning via Proof Planning in it; thirdly, we show a set of experimental results obtained by applying the framework to the problem of Feature Interactions in telecommunication systems. These results indicate that (a) the problem can be concisely and effectively modeled in the aforementioned logic, (b) proof planning actually captures common structures in the related proofs, and (c) the approach is viable also from the point of view of efficiency.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Automated Reasoning in Quantified Modal and Temporal Logics

Descriviamo in questo articolo la tesi di dottorato dell’autore, centrata sul ragionamento automatico nelle logiche modali e temporali quantificate. I contributi originali della tesi sono: (i) la formulazione di una famiglia di calcoli di sequenti corretti e completi per le logiche modali quantificate; (ii) l’estensione dell’approccio alla logica temporale quantificata del tempo lineare e discreto, e la creazione di un framework per il ragionamento automatico in essa basato sul Proof Planning; (iii) risultati sperimentali ottenuti applicando il suddetto framework al problema delle Feature Interactions nei sistemi di telecomunicazioni. We report on the author’s Ph.D. thesis, concerned with automated reasoning in quantified modal and temporal logics. The relevant contributions are three: (i) we devise a sound and complete set of sequent calculi for quantified modal logics; (ii) we extend the approach to the quantified temporal logic of linear, discrete time and develop a framework for doing automated reasoning via Proof Planning in it; (iii) we show a set of experimental results obtained by applying the framework to the problem of Feature Interactions in telecommunication systems

Proof Analysis in Temporal Logic

The logic of time is one of the most interesting modal logics, and its importance is widely acknowledged both for philosophical and formal reasons. In this thesis, we apply the method of internalisation of Kripke-style semantics into the syntax of sequent calculus to the proof-theoretical analysis of temporal logics. Sequent systems for different flows of time are obtained as modular extensions of a basic temporal calculus, through the addition of appropriate mathematical rules that correspond to the properties of temporal frames: a general and uniform treatment is thus achieved for a wide range of temporal logics. All the calculi enjoy remarkable structural properties, in particular are contraction and cut free. Linear discrete time is analysed by means of two infinitary calculi. The first is obtained by means of a rule with infinitely many premises, and the second through a new definition of provability which admits, under certain conditions, derivation trees with infinite branches. The first calculus enjoys the desired structural properties, but the presence of an infinitary rule is harmful for proof analysis. Two finitary systems are identified by replacing the infinitary rule with a weaker finitary rule, and by bounding the number of its premises, respectively. Corresponding, somehow complementary, conservativity results are proved with respect to adequate fragments of the original calculus. The second calculus stems from a closure algorithm which exploits the fixed-point equations for temporal operators and gives saturated sets of closure formulas from a given formula. Finitisation is obtained in the form of an upper bound to the proof-search procedure, and decidability follows as a major consequence