Academic literature on the topic 'Hybrid Hoare logic'

There is both a great unity and a great diversity in presentations of logic. The diversity is staggering indeed – propositional logic, first-order logic, higher-order logic belong to one classification; linear logic, intuitionistic logic, classical logic, modal and temporal logics belong to another one. Logical deduction may be presented as a Hilbert style of combinators, as a natural deduction system, as sequent calculus, as proof nets of one variety or other, etc. Logic, originally a field of philosophy, turned into algebra with Boole, and more generally into meta-mathematics with Frege and Heyting. Professional logicians such as Gödel and later Tarski studied mathematical models, consistency and completeness, computability and complexity issues, set theory and foundations, etc. Logic became a very technical area of mathematical research in the last half century, with fine-grained analysis of expressiveness of subtheories of arithmetic or set theory, detailed analysis of well-foundedness through ordinal notations, logical complexity, etc. Meanwhile, computer modelling developed a need for concrete uses of logic, first for the design of computer circuits, then more widely for increasing the reliability of sofware through the use of formal specifications and proofs of correctness of computer programs. This gave rise to more exotic logics, such as dynamic logic, Hoare-style logic of axiomatic semantics, logics of partial values (such as Scott's denotational semantics and Plotkin's domain theory) or of partial terms (such as Feferman's free logic), etc. The first actual attempts at mechanisation of logical reasoning through the resolution principle (automated theorem proving) had been disappointing, but their shortcomings gave rise to a considerable body of research, developing detailed knowledge about equational reasoning through canonical simplification (rewriting theory) and proofs by induction (following Boyer and Moore successful integration of primitive recursive arithmetic within the LISP programming language). The special case of Horn clauses gave rise to a new paradigm of non-deterministic programming, called Logic Programming, developing later into Constraint Programming, blurring further the scope of logic. In order to study knowledge acquisition, researchers in artificial intelligence and computational linguistics studied exotic versions of modal logics such as Montague intentional logic, epistemic logic, dynamic logic or hybrid logic. Some others tried to capture common sense, and modeled the revision of beliefs with so-called non-monotonic logics. For the careful crafstmen of mathematical logic, this was the final outrage, and Girard gave his anathema to such “montres à moutardes”.

La modélisation de systèmes biologiques est devenue indispensable pour comprendre les phénomènes complexes et émergents issus d'influences partiellement connues, et pour envisager de contrôler un système altéré dans le but de restaurer un comportement physiologique. Tout modèle, quel que soit son paradigme sous-jacent, fait intervenir des paramètres gouvernant sa dynamique mais les mesures expérimentales ne permettent généralement pas de les identifier et cela reste l'un des problèmes majeurs de la modélisation. Cette thèse propose une méthode automatique d'identification des paramètres dynamiques de systèmes biologiques dans un cadre de modélisation hybride. Le cadre hybride choisi découpe l'espace des phases selon l'activité des entités biologiques, et associe à chacun de ces sous-espaces une vitesse d'évolution de chacun des composants. Nous proposons une logique de Hoare en temps continu ainsi qu'un calcul de plus faible précondition qui, à partir d'observations expérimentales qualitatives et chronométriques, construit les contraintes minimales sur les paramètres du modèle pour qu’il soit compatible avec les observations. Ce calcul mène à un problème de satisfaction de contraintes sur les réels et nous montrons que celui-ci peut être résolu par le solveur AbSolute.Le prototype Holmes BioNet développé au cours de cette thèse peut non seulement automatiser le processus d'identification des valeurs des paramètres à partir des observations expérimentales, mais aussi simuler l'évolution du modèle obtenu afin de le comparer avec les traces expérimentales. Nous utilisons ce prototype pour modéliser le couplage des cycles cellulaire et circadien<br>Modelling biological systems has become instrumental to understand complex and emerging phenomena resulting from partially known influences, and to consider controlling an altered system in order to restore a physiological behaviour. Any model, independent of the underlying paradigm, involves parameters governing its dynamics. However, experimental measurements generally do not allow their identification and this remains one of the major problems of modelling. This PhD proposes an automatic method for identifying the dynamic parameters of biological systems in a hybrid modelling framework. The chosen hybrid framework splits the phase space according to the activity of the biological entities, and associates to each of these subspaces a celerity for each of the components. We introduce a continuous time Hoare logic as well as its weakest precondition calculus which, from qualitative and chronometrical experimental observations, constructs the minimum constraints on the model parameters making it compatible with the observations. This calculus leads to a Constraint Satisfaction Problem on real numbers and we show that it can be solved by the AbSolute solver.The Holmes BioNet prototype developed during this PhD can not only automate the parameter identification process from experimental data, but also simulate the evolution of the obtained model in order to compare it with experimental traces. We use this prototype to model the coupling of the cellular and circadian cycles