Books on the topic 'Higher-order logic'

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1

Gopalan, Nadathur, ed. Programming with higher-order logic. Cambridge: Cambridge University Press, 2012.

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2

Paulson, Lawrence C. The representation of logics in higher-order logic. Cambridge: University of Cambridge, Computer Laboratory, 1987.

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3

Higher order logic and hardware verification. Cambridge: Cambridge University Press, 1993.

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4

Camilleri, Albert. Hardware verification using higher-order logic. Cambridge: University of Cambridge, Computer Laboratory, 1986.

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5

J, Scott P., ed. Introduction to higher order categorical logic. Cambridge [Cambridgeshire]: Cambridge University Press, 1986.

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6

Lambek, J. Introduction to higher order catagorical logic. Cambridge: CUP, 1986.

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7

Heering, Jan, Karl Meinke, Bernhard Möller, and Tobias Nipkow, eds. Higher-Order Algebra, Logic, and Term Rewriting. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58233-9.

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8

Dowek, Gilles, Jan Heering, Karl Meinke, and Bernhard Möller, eds. Higher-Order Algebra, Logic, and Term Rewriting. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61254-8.

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9

Solving higher-order equations: From logic to programming. Boston: Birkhauser, 1998.

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10

Joyce, Jeffrey. Proving a computer correct in higher order logic. Cambridge: University of Cambridge, Computer Laboratory, 1986.

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11

Gordon, M. J. C. A proof generating system for higher-order logic. Cambridge: University of Cambridge, Computer Laboratory, 1987.

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12

Thomas Schubert, E., Philip J. Windley, and James Alves-Foss, eds. Higher Order Logic Theorem Proving and Its Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60275-5.

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13

Joyce, Jeffrey J., and Carl-Johan H. Seger, eds. Higher Order Logic Theorem Proving and Its Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57826-9.

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14

Melham, Thomas F., and Juanito Camilleri, eds. Higher Order Logic Theorem Proving and Its Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58450-1.

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15

Gordon, M. J. C. HOL, a machine orientated formulation of higher order logic. Cambridge: University of Cambridge, ComputerLaboratory, 1985.

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16

IFIP TC10/WG10.2 International Workshop on Higher Order Logic Theorem Proving and Its Applications (1992 Leuven, Belgium). Higher order logic theorem proving and its applications: Proceedings of the IFIP TC10/WG10.2 International Workshop on Higher Order Logic Theorem Proving and Its Applications--HOL '92. Amsterdam: North-Holland, 1993.

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17

TPHOLs '98 (1998 Canberra, A.C.T.). Theorem proving in higher order logics: 11th international conference, TPHOLs '98, Canberra, Australia, September 27-October 1, 1998 : proceedings. Berlin: Springer, 1998.

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18

1967-, Schneider Klaus, and Brandt Jens 1978-, eds. Theorem proving in higher order logics: 20th international conference, TPHOLs 2007, Kaiserslautern, Germany, September 10-13, 2007 ; proceedings. Berlin: Springer, 2007.

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19

Makarius, Wenzel, Urban Christian, Nipkow Tobias, and SpringerLink (Online service), eds. Theorem Proving in Higher Order Logics: 22nd International Conference, TPHOLs 2009, Munich, Germany, August 17-20, 2009. Proceedings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009.

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20

1959-, Schubert E. Thomas, Windley Phillip J. 1958-, and Alves-Foss James 1964-, eds. Higher order logic theorem proving and its applications: 8th International Workshop, Aspen Grove, UT, USA, September 11-14, 1995 : proceedings. Berlin: Springer-Verlag, 1995.

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21

TPHOLs '97 (1997 Murray Hill, N.J.). Theorem proving in higher order logics: 10th international conference, TPHOLs '97, Murray Hill, NJ, USA, August 19-22, 1997 : proceedings. Berlin: Springer, 1997.

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22

Wong, Wai. A formal theory of railway track networks in higher-order logic and its applications in interlocking design. [s.l.]: typescript, 1992.

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23

F, Melham T., and Camilleri Juanito, eds. Higher order logic theorem proving and its applications: 7th international workshop, Valletta, Malta, September 19-22, 1994 : proceedings. Berlin: Springer-Verlag, 1994.

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24

J, Heering, and International Workshop on Higher-Order Algebra, Logic, and Term Rewriting (1st : 1993 : Amsterdam, Netherlands), eds. Higher-order algebra, logic, and term rewriting: First international workshop, HOA '93, Amsterdam The Netherlands, September 23-24, 1993 : selected papers. Berlin: Springer-Verlag, 1994.

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25

David, Hutchison. Theorem Proving in Higher Order Logics: 21st International Conference, TPHOLs 2008, Montreal, Canada, August 18-21, 2008. Proceedings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008.

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26

1960-, Joyce Jeffrey J., Seger Carl-Johan H, and HOL User's Group Workshop (6th : 1993 : Vancouver, B.C.), eds. Higher order logic theorem proving and its applications: 6th International Workshop, HUG '93, Vancouver, B.C., Canada, August 11-13, 1993 : proceedings. Berlin: Springer-Verlag, 1994.

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27

Bertot, Yves, Gilles Dowek, Laurent Théry, André Hirschowitz, and Christine Paulin, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48256-3.

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28

Schneider, Klaus, and Jens Brandt, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-74591-4.

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29

Berghofer, Stefan, Tobias Nipkow, Christian Urban, and Makarius Wenzel, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03359-9.

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30

Aagaard, Mark, and John Harrison, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44659-1.

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31

Boulton, Richard J., and Paul B. Jackson, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44755-5.

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32

Hurd, Joe, and Tom Melham, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11541868.

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33

Gunter, Elsa L., and Amy Felty, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0028381.

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34

Goos, Gerhard, Juris Hartmanis, Jan van Leeuwen, Joakim von Wright, Jim Grundy, and John Harrison, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0105392.

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35

Grundy, Jim, and Malcolm Newey, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0055125.

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36

Carreño, Victor A., César A. Muñoz, and Sofiène Tahar, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45685-6.

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37

Slind, Konrad, Annette Bunker, and Ganesh Gopalakrishnan, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/b100400.

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38

Basin, David, and Burkhart Wolff, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/b11935.

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39

Mohamed, Otmane Ait, César Muñoz, and Sofiène Tahar, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71067-7.

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40

Shapiro, Stewart. Higher‐order Logic. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0025.

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The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that. It develops the syntax of second-order languages and present typical deductive systems and model-theoretic semantics for them. This will help to explain the role of higher-order logic in the philosophy of mathematics. It is assumed that the reader has at least a passing familiarity with the theory and metatheory of first-order logic.
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41

Jané, Ignacio. Higher‐order Logic Reconsidered. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0026.

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This article discusses canonical (i.e., full, or standard) second-order consequence and argues against it being a case of logical consequence. The discussion is divided into three parts. The first part comprises the first three sections. After stating the problem in Section 1, Sections 2 and 3 examine the role that the consequence relation is expected to play in axiomatic theories. This leads to put forward two requirements on logical consequence, which are called “formality” and “noninterference.” It is this last requirement that canonical second-order consequence violates, as the article sets out to substantiate. The fourth section argues that canonical second-order logic is inadequate for axiomatizing set theory, on the grounds that it codes a significant amount of set-theoretical content.
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42

Nadathur, Gopalan, and Dale Miller. Programming with Higher-Order Logic. Cambridge University Press, 2012.

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43

Nadathur, Gopalan, and Dale Miller. Programming with Higher-Order Logic. Cambridge University Press, 2012.

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44

Nadathur, Gopalan, and Dale Miller. Programming with Higher-Order Logic. Cambridge University Press, 2012.

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45

Nadathur, Gopalan, and Dale Miller. Programming with Higher-Order Logic. Cambridge University Press, 2012.

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46

Gallin, Daniel. Intensional and Higher-Order Modal Logic. Elsevier Science & Technology Books, 2016.

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47

Bell, John L. Higher-Order Logic and Type Theory. Cambridge University Press, 2022.

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48

Melham, T. F. Higher Order Logic and Hardware Verification. Cambridge Univ Pr, 2009.

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49

Melham, T. F. Higher Order Logic and Hardware Verification. Cambridge University Press, 2010.

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50

Bell, John L. Higher-Order Logic and Type Theory. Cambridge University Press, 2022.

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