9,851 research outputs found

    Theorem proving with built-in hybrid theories

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    A growing number of applications of automated reasoning exhibits the necessity of flexible deduction systems. A deduction system should be able to execute inference rules which are appropriate to the given problem. One way to achieve this behavior is the integration of different calculi. This led to so called hybrid reasoning [22, 1, 10, 20] which means the integration of a general purpose foreground reasoner with a specialized background reasoner. A typical task of a background reasoner is to perform special purpose inference rules according to a built-in theory. The aim of this paper is to go a step further, i.e. to treat the background reasoner as a hybrid system itself. The paper formulates sufficient criteria for the construction of complete calculi which enable reasoning under hybrid theories combined from sub-theories. For this purpose we use a generic approach described in [20]. This more detailed view on built-in theories is not covered by the known general approaches [1, 3, 6, 20] for building in theories into theorem provers. The approach is demonstrated by its application to the target calculi of the algebraic translation [9] of multi-modal and extended multi-modal [7] logic to first-order logic

    Tool support for reasoning in display calculi

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    We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, that allows us to adapt the tool for a wide variety of user defined calculi

    Actor Network Procedures as Psi-calculi for Security Ceremonies

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    The actor network procedures of Pavlovic and Meadows are a recent graphical formalism developed for describing security ceremonies and for reasoning about their security properties. The present work studies the relations of the actor network procedures (ANP) to the recent psi-calculi framework. Psi-calculi is a parametric formalism where calculi like spi- or applied-pi are found as instances. Psi-calculi are operational and largely non-graphical, but have strong foundation based on the theory of nominal sets and process algebras. One purpose of the present work is to give a semantics to ANP through psi-calculi. Another aim was to give a graphical language for a psi-calculus instance for security ceremonies. At the same time, this work provides more insight into the details of the ANPs formalization and the graphical representation.Comment: In Proceedings GraMSec 2014, arXiv:1404.163

    Automated Synthesis of Tableau Calculi

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    This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

    MetTeL: A Generic Tableau Prover.

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    Algebraic Properties of Qualitative Spatio-Temporal Calculi

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    Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia
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