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Higher-Order Tableaux (1995)  (Make Corrections)  (19 citations)
Michael Kohlhase
Analytic Tableaux and Related Methods



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Abstract: . Even though higher-order calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higher-order logic that use higher-order unification as the key inference procedure. These calculi differ in the treatment of the substitutional properties of equivalences. The first calculus is equivalent in deductive power to the machineoriented higher-order refutation calculi known from the literature,... (Update)

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...completeness. As a consequence, the calculi developed for higher order automated theorem proving [And71, Hue72, Hue73, JP72, Mil83, Koh94b, Koh95] and the corresponding theorem proving systems such as Tps [ABI 96] or earlier versions of the authors Leo 1 are not or cannot be...

.... Func analogously reflects functional extensionality: if two functions are not equal then there exists an argument s ff on which 9 [Koh95] presents a tableaux calculus analogous to HORES that aims to reach Henkin completeness without extensionality by adding rule Equiv. But...

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Dynamic Lambda Calculus - Michael Kohlhase Susanna   (Correct)
A Simple Deduction System for First-Order Logic with.. - Goubault-Larrecq (1999)   (Correct)
Henkin Completeness of Higher-Order Resolution - Benzmüller, Kohlhase (1997)   (Correct)

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10:   An unification algorithm for typed -calculus (context) - Huet - 1975
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BibTeX entry:   (Update)

Michael Kohlhase. Higher-order tableaux. In Proceedings of the Tableau Workshop, pages 294--309, Koblenz, Germany, 1995. http://citeseer.ist.psu.edu/article/kohlhase95higherorder.html   More

@inproceedings{ kohlhase95higherorder,
    author = "Michael Kohlhase",
    title = "Higher-Order Tableaux",
    booktitle = "Analytic Tableaux and Related Methods",
    pages = "294-309",
    year = "1995",
    url = "citeseer.ist.psu.edu/article/kohlhase95higherorder.html" }
Citations (may not include all citations):
729   The Lambda-Calculus: Its Syntax and Semantics (context) - Barendregt - 1980
235   First-Order Logic (context) - Smullyan - 1968
86   Completeness in the theory of types (context) - Henkin - 1950
68   Uber formal unentscheidbare Satze der Principia Mathematica .. (context) - Godel - 1931
47   Introduction to Combinators and Lambda Calculus (context) - Hindely, Seldin - 1986
42   Resolution in type theory (context) - Andrews - 1971
28   An improved proof procedure (context) - Prawitz - 1960
28   Proofs in Higher-Order Logic (context) - Miller - 1983
27   Constrained Resolution: A Complete Method for Higher Order L.. (context) - Huet - 1972
24   Equations dans des Langages d'ordre (context) - Huet - 1976
24   A Mechanization of Sorted Higher-Order Logic Based on the Re.. (context) - Kohlhase - 1994
23   Proof Transformations in Higher-Order Logic (context) - Pfenning - 1987
20   order type theory through unification (context) - Jensen, Pietrzykowski - 1976
20   On connections and higher order logic (context) - Andrews - 1989
16   Acta Philosophica Fennica (context) - Hintikka, content et al. - 1955
11   Progress in Computer Science and Applied Logic (context) - Snyder, Theory et al. - 1991
10   Semantic tableaux as a framework for automated theorem-provi.. (context) - Reeves - 1987
7   A unifying principle for quantification theory (context) - Smullyan - 1963
6   First-Order Logic and Automated Threorem Proving (context) - Fitting - 1990
3   letter to Roger Hindley dated January 22 (context) - Andrews - 1973
2   Medelingen von de Koninklijke Nederlandse Akademie van Weten.. (context) - Beth, formla - 1955
1   Semantic entailmentand formla derivability (context) - Beth - 1969



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