211 research outputs found

    A Generic Framework for Implicate Generation Modulo Theories

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    International audienceThe clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that generates the implicates of a quantifier-free formula modulo a theory. No assumption is made on the considered theory, other than the existence of a decision procedure. The algorithm has been implemented (using the solvers MiniSAT, CVC4 and Z3) and experimental results show evidence of the practical relevance of the proposed approach

    Ilinva: Using Abduction to Generate Loop Invariants

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    International audienceWe describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize in-ductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large set of programming languages and application domains; and lazy, in the sense that it only generates invariants that allow one to derive the required properties. It relies on an existing system called GPiD for abductive reasoning modulo theories [14], and on the platform for program verification Why3 [16]. Experiments show evidence of the practical relevance of our approach

    Abduction in {EL} via Translation to {FOL}

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    International audienceWe present a technique for performing TBox abduction in the description logic EL. The input problem is converted into first-order formulas on which a prime implicate generation technique is applied, then EL hypotheses are reconstructed by combining the generated positive and negative implicates

    Lorenz, G\"{o}del and Penrose: New perspectives on determinism and causality in fundamental physics

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    Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of Lorenz's fractal invariant set relate space-time calculus to deep areas of mathematics such as G\"{o}del's Incompleteness Theorem. These properties, combined with some recent developments in theoretical and observational cosmology, motivate what is referred to as the `cosmological invariant set postulate': that the universe UU can be considered a deterministic dynamical system evolving on a causal measure-zero fractal invariant set IUI_U in its state space. Symbolic representations of IUI_U are constructed explicitly based on permutation representations of quaternions. The resulting `invariant set theory' provides some new perspectives on determinism and causality in fundamental physics. For example, whilst the cosmological invariant set appears to have a rich enough structure to allow a description of quantum probability, its measure-zero character ensures it is sparse enough to prevent invariant set theory being constrained by the Bell inequality (consistent with a partial violation of the so-called measurement independence postulate). The primacy of geometry as embodied in the proposed theory extends the principles underpinning general relativity. As a result, the physical basis for contemporary programmes which apply standard field quantisation to some putative gravitational lagrangian is questioned. Consistent with Penrose's suggestion of a deterministic but non-computable theory of fundamental physics, a `gravitational theory of the quantum' is proposed based on the geometry of IUI_U, with potential observational consequences for the dark universe.Comment: This manuscript has been accepted for publication in Contemporary Physics and is based on the author's 9th Dennis Sciama Lecture, given in Oxford and Triest

    Improved False Causal Loop Detection in Polychronous Specificationof Embedded Software

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    As opposed to single clocked synchronous programming paradigms, polychronous formalism allows specification of concurrent data flow computation on signals such that various data flows can evolve asynchronous with respect to each other. Explicit constraints and constraints implied by the syntactic structures impart certain intrinsic properties to models specified polychronously. One of the major steps in designing a synthesis engine for polychronous specifications is the characterization of specified models into categories such as inherently sequential or inherently multi-threaded. In this paper, we are concerned with sequentially implementable polychronous specification where computation is divided into a totally ordered sequence of logical instants. Data flow computation within an instant happens based on the implied data flow order. This order or data dependency often varies from one instant to another. Thus determining if there is an instant at which the data flow order forms a causal cycle is an important problem. In the current polychronous compilers, such as SIGNAL compiler and EmCodeSyn, this is solved without due effort, by rejecting any program which has a buffer-free structural cycle. However, a clocked dependency graph can be used to construct logical constraints representing the instants with a possible causal loop. The satisfiability of such constraints would imply that such a loop is realizable and hence the specification has a possible deadlock. The reachability of this instant with a given set of initial conditions would verify if the program should be rejected. In the past, the work on such constraints and their satisfiability has not been implemented even though for pure Boolean signals and clocks this could have been done using a satisfiability solver. With the advent to SAT modulo theory (SMT) solvers, this can now be extended to a more general class of specifications. Moreover, model checking on an abstraction of the specification can provide more information about the reachability of instants at which cyclic data dependency is realized. This paper presents an improved polychronous synthesis tool accepting a much larger class of specifications than could be done before. In our experimental results, we demonstrate the capabilities of our causality analysis methods and show that our synthesis tool performs better than previous strategies, including our own past work

    Connection-Minimal Abduction in EL\mathcal{EL} via Translation to {FOL}

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    International audienceAbduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible explanations for unexpected observations. We consider TBox abduction in the lightweight description logic EL , where the observation is a concept inclusion and the background knowledge is a TBox, i.e., a set of concept inclusions. To avoid useless answers, such problems usually come with further restrictions on the solution space and/or minimality criteria that help sort the chaff from the grain. We argue that existing minimality notions are insufficient, and introduce connection minimality. This criterion follows Occam’s razor by rejecting hypotheses that use concept inclusions unrelated to the problem at hand. We show how to compute a special class of connection-minimal hypotheses in a sound and complete way. Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates. We evaluate a prototype implementation of our approach on ontologies from the medical domain

    Connection-minimal Abduction in EL via Translation to FOL -- Technical Report

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    Abduction in description logics finds extensions of a knowledge base to makeit entail an observation. As such, it can be used to explain why theobservation does not follow, to repair incomplete knowledge bases, and toprovide possible explanations for unexpected observations. We consider TBoxabduction in the lightweight description logic EL, where the observation is aconcept inclusion and the background knowledge is a TBox, i.e., a set ofconcept inclusions. To avoid useless answers, such problems usually come withfurther restrictions on the solution space and/or minimality criteria that helpsort the chaff from the grain. We argue that existing minimality notions areinsufficient, and introduce connection minimality. This criterion followsOccam's razor by rejecting hypotheses that use concept inclusions unrelated tothe problem at hand. We show how to compute a special class ofconnection-minimal hypotheses in a sound and complete way. Our technique isbased on a translation to first-order logic, and constructs hypotheses based onprime implicates. We evaluate a prototype implementation of our approach onontologies from the medical domain.<br

    Abduction inELvia Translation to FOL

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    International audienceWe present a technique for performing TBox abduction in the description logic EL. The input problem is converted into first-order formulas on which a prime implicate generation technique is applied, then EL hypotheses are reconstructed by combining the generated positive and negative implicates
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