23 research outputs found

    Formalization of the fundamental group in untyped set theory using auto2

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    We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

    Deduction-Based Software Component Retrieval

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    Deduction-based software component retrieval is a software reuse technique that uses formal specifications as component descriptors and as search keys; matching components are identified using an automated theorem prover. This dissertation contains a detailed theoretical investigation of the concept as well as the first substantial experimental evaluation of its technical feasibility.Deduktionsbasiertes Kompenentenretrieval ist eine Softwarereusetechnik, in der formale Spezifikationen zur Beschreibung von Komponenten sowie als Anfragen verwendet werden; passende Komponenten werden mit Hilfe eines automatischen Theorembeweisers ermittelt. Diese Arbeit enthält eine detaillierte theoretische Untersuchung dieses Konzeptes und die erste ausführliche experimentelle Evaluierung seiner technischen Realisierbarkeit

    Verification of Model Transformations

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    With the increasing use of automatic transformations of models, the correctness of these transformations becomes an increasingly important issue. Especially for model transformation generally defined using abstract description techniques like graph transformations or declarative relational specifications, however, establishing the soundness of those transformations by test-based approaches is not straight-forward. We show how formal verification of soundness conditions over such declarative relational style transformations can be performed using an interactive theorem prover. The relational style allows a direct translation of transformations as well as associated soundness conditions into corresponding axioms and theorems. Using the Isabelle theorem prover, the approach is demonstrated for a refactoring transformation and a connectedness soundness condition

    LISA - A Modern Proof System

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    Verifying Programs with Logic and Extended Proof Rules: Deep Embedding v.s. Shallow Embedding

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    Many foundational program verification tools have been developed to build machine-checked program correctness proofs, a majority of which are based on Hoare logic. Their program logics, their assertion languages, and their underlying programming languages can be formalized by either a shallow embedding or a deep embedding. Tools like Iris and early versions of Verified Software Toolchain (VST) choose different shallow embeddings to formalize their program logics. But the pros and cons of these different embeddings were not yet well studied. Therefore, we want to study the impact of the program logic's embedding on logic's proof rules in this paper. This paper considers a set of useful extended proof rules, and four different logic embeddings: one deep embedding and three common shallow embeddings. We prove the validity of these extended rules under these embeddings and discuss their main challenges. Furthermore, we propose a method to lift existing shallowly embedded logics to deeply embedded ones to greatly simplify proofs of extended rules in specific proof systems. We evaluate our results on two existing verification tools. We lift the originally shallowly embedded VST to our deeply embedded VST to support extended rules, and we implement Iris-CF and deeply embedded Iris-Imp based on the Iris framework to evaluate our theory in real verification projects

    Range-Restricted Interpolation through Clausal Tableaux

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    We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are induced by a restriction of the clausal tableau structure, which can be achieved in general by a proof transformation, also if the source proof is by resolution/paramodulation. Primarily addressed applications are query synthesis and reformulation with interpolation. Our methodical approach combines operations on proof structures with the immediate perspective of feasible implementation through incorporating highly optimized first-order provers

    Using Cognitive Entropy to Manage Uncertain Concepts in Formal Ontologies

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    A logical formalism to support the insertion of uncertain concepts in formal ontologies is presented. It is based on the search of extensions by means of two automated reasoning systems (ARS), and it is driven by what we call cognitive entropy.Ministerio de Educación y Ciencia TIN2004-0388
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