A more expressive formulation of many sorted logic

Cohn, Anthony G.

doi:10.1007/bf00243207

Cited by 76 publications

(41 citation statements)

References 30 publications

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“…While the development of the TPTP World for typed first-order logic is new, several similar logics have been described previously, e.g., [36,26,13]. However, there are no contemporary ATP systems that implement those logics.…”

Section: Motivation and Historymentioning

confidence: 98%

“…The problems came from various sources. Firstly, problems were found in the many papers that describe type systems, e.g., [36,13]. Not all the problems were suitable, mainly because they employ subtyping, but others were translated to the TFF0 syntax.…”

Section: Tff Problems Atp Systems Tptp Softwarementioning

confidence: 99%

“…Problems that use these new features have been added to the TPTP problem library, and ATP systems that can solve these problems have been developed. This paper describes the key steps of these developments.While the development of the TPTP World for typed first-order logic is new, several similar logics have been described previously, e.g., [36,26,13]. However, there are no contemporary ATP systems that implement those logics.…”

mentioning

confidence: 98%

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The TPTP Typed First-Order Form with Arithmetic

Sutcliffe

Schulz

Claessen

et al. 2012

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. The TPTP World is a well established infrastructure supporting research, development, and deployment of Automated Theorem Proving systems. Recently, the TPTP World has been extended to include a typed first-order logic, which in turn has enabled the integration of arithmetic. This paper describes these developments. Motivation and HistoryThe TPTP World [32] is a well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The TPTP World is based on the Thousands of Problems for Theorem Provers (TPTP) problem library [30], and includes the TPTP language, the SZS ontologies, the Thousands of Solutions from Theorem Provers (TSTP) solution library, various tools associated with the libraries, and the CADE ATP System Competition (CASC). This infrastructure has been central to the progress that has been made in the development of high performance first-order ATP systems -most state of the art systems natively read the TPTP language, many produce proofs or models in the TSTP format, much testing and development is done using the TPTP problem library, and CASC is an annual focal point where developers meet to discuss new ideas and advances in ATP techniques.Originally the TPTP supported only first-order problems in clause normal form (CNF). Over the years support for the full first-order form (FOF) and typed higher-order form (THF) have been added. Recently the simply typed first-order form (TFF) has been added. TFF has in turn been used as the basis for supporting arithmetic. Problems that use these new features have been added to the TPTP problem library, and ATP systems that can solve these problems have been developed. This paper describes the key steps of these developments.While the development of the TPTP World for typed first-order logic is new, several similar logics have been described previously, e.g., [36,26,13]. However, there are no contemporary ATP systems that implement those logics. There is active related research in the SMT community, which started in 2003 [24]. There are high performance systems for the various logics of the SMT-LIB 1 , e.g., those1 See the SMT-LIB web page

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Section: Motivation and Historymentioning

confidence: 98%

Section: Tff Problems Atp Systems Tptp Softwarementioning

confidence: 99%

mentioning

confidence: 98%

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The TPTP Typed First-Order Form with Arithmetic

Sutcliffe

Schulz

Claessen

et al. 2012

Logic for Programming, Artificial Intelligence, and Reasoning

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“…There is some variation in the full set of axioms used for the RCC theory. The formal apparatus of the original theory is complicated by the use of the many-sorted logic LLAMA [18] and the use of a non-standard definite description operator (ιx[ϕ(x)]). This makes it difficult to make a direct comparison with the algebraically based theories presented in the current paper.…”

Section: The Region Connection Calculusmentioning

confidence: 99%

Axioms, Algebras and Topology

Bennett

Düntsch²

2007

Handbook of Spatial Logics

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“…In this way the order-sorted logics arise (Cohn, 1987;Walther, 1987;Schmidt-Schauss, 1989), in which deductions take note of the sort hierarchy. In them, this sort hierarchy is statically fixed by the signature and is only used when the process of unification obtains substitutions.…”

Section: Introductionmentioning

confidence: 98%

Tableau Methods for a Logic with Term Declarations

Martin

Gavilanes

Leach

2000

Journal of Symbolic Computation

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We study free variable tableau methods for logics with term declarations. We show how to define a substitutivity rule preserving the soundness of the tableaux and we prove that some other attempts lead to unsound systems. Based on this rule, we define a sound and complete free variable tableau system and we show how to restrict its application to close branches by defining a sorted unification calculus.

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A more expressive formulation of many sorted logic

Cited by 76 publications

References 30 publications

The TPTP Typed First-Order Form with Arithmetic

The TPTP Typed First-Order Form with Arithmetic

Axioms, Algebras and Topology

Tableau Methods for a Logic with Term Declarations

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