Notre Dame Journal of Formal Logic

Computing Verisimilitude

Katarina Britz and Chris Brink

Source: Notre Dame J. Formal Logic Volume 36, Number 1 (1995), 30-43.

Abstract

This paper continues the power ordering approach to verisimilitude. We define a parameterized verisimilar ordering of theories in the finite propositional case, both semantically and syntactically. The syntactic definition leads to an algorithm for computing verisimilitude. Since the power ordering approach to verisimilitude can be translated into a standard notion of belief revision, the algorithm thereby also allows the computation of membership of a belief-revised theory.

Primary Subjects: 03B60
Secondary Subjects: 68T27
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040308827
Mathematical Reviews number (MathSciNet): MR1359106
Digital Object Identifier: doi:10.1305/ndjfl/1040308827
Zentralblatt MATH identifier: 0837.03009

References

[1] Andrews, P. B., An Introduction to Mathematical Logic and Type Theory: to Truth through Proof, Computer Science and Applied Mathematics Series, Academic Press, Orlando, 1986.
Mathematical Reviews (MathSciNet): MR88g:03001
Zentralblatt MATH: 0617.03001
[2] Barwise, J., editor, Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland, Amsterdam, 1977.
Mathematical Reviews (MathSciNet): MR56:15351
Zentralblatt MATH: 0443.03001
[3] Brink, C., ``Verisimilitude: views and reviews,'' History and Philosophy of Logic, vol. 10 (1989), pp. 181--201.
Mathematical Reviews (MathSciNet): MR90k:03003
Zentralblatt MATH: 0674.03002
Digital Object Identifier: doi:10.1080/014453408908837149
[4] Brink, C., ``Power structures,'' Algebra Universalis, vol. 30 (1993), pp. 177--216.
Mathematical Reviews (MathSciNet): MR94g:08002
Zentralblatt MATH: 0787.08001
Digital Object Identifier: doi:10.1007/BF01196091
[5] Brink, C., and J. Heidema, ``A versimilar ordering of theories phrased in a propositional language,'' British Journal for the Philosophy of Science, vol. 38 (1987), pp. 533--549.
Zentralblatt MATH: 0676.03001
Mathematical Reviews (MathSciNet): MR932843
Digital Object Identifier: doi:10.1093/bjps/38.4.533
[6] Brink, C., and J. Heidema, ``A verisimilar ordering of propositional theories: the infinite case,'' Technical Report TR-ARP-1/89, Research School of Social Sciences, Australian National University, Canberra, 1989.
[7] Brink, C., J. J. C. Vermeulen, and J. P. G. Pretorius, ``Verisimilitude via vietoris,'' Journal of Logic and Computation, vol. 2 (1992), pp. 709--718.
Mathematical Reviews (MathSciNet): MR94g:03017
Zentralblatt MATH: 0774.03010
Digital Object Identifier: doi:10.1093/logcom/2.6.709
[8] Burger, I. C., and J. Heidema, ``Comparing theories by their positive and negative contents,'' The British Journal for the Philosophy of Science, vol. 44 (1993), pp. 605--630.
Mathematical Reviews (MathSciNet): MR95e:03036
Digital Object Identifier: doi:10.1093/bjps/45.2.605
[9] Makinson, D., and P. Gärdenfors, ``Relations between the logic of theory change and nonmonotonic logic,'' pp. 185--205 in The Logic of Theory Change, edited by A. Fuhrmann and M. Morreau, Lecture Notes in Artificial Intelligence, vol. 465, Springer-Verlag, Berlin, 1991.
Mathematical Reviews (MathSciNet): MR1096795
Zentralblatt MATH: 0925.03130
Digital Object Identifier: doi:10.1007/BFb0018421
[10] Miller, D., ``Popper's qualitative theory of verisimilitude,'' British Journal for the Philosophy of Science, vol. 25 (1974), pp. 166--177.
Zentralblatt MATH: 0377.02007
[11] Popper, K. R., Conjectures and Refutations, Routledge and Kegan Paul, London, 1963.
Mathematical Reviews (MathSciNet): MR27:2393
[12] Ryan, M. D., ``Defaults and revision in structured theories,'' pp. 362--373 in Proceedings Sixth IEEE Symposium on Logic in Computer Science (LICS), IEEE, Amsterdam, 1991.
[13] Ryan, M. D., and P.-Y. Schobbens, ``Belief revision and verisimilitude,'' Notre Dame Journal of Formal Logic, vol. 36 (1995), pp. 15--29.
Mathematical Reviews (MathSciNet): MR96k:03071
Zentralblatt MATH: 0837.03008
Digital Object Identifier: doi:10.1305/ndjfl/1040308826
Project Euclid: euclid.ndjfl/1040308826
[14] Schurz, G., and P. Weingartner, ``Verisimilitude defined by relevant consequence-elements,'' pp. 47--77 in What is closer-to-the-truth?, Rodopi, Amsterdam, 1987.
[15] Shoham, Y., Reasoning about Change, MIT Press, Cambridge, 1988.
Mathematical Reviews (MathSciNet): MR90b:68081
[16] Tichý, P., ``On Popper's definitions of verisimilitude,'' British Journal for the Philosophy of Science, vol. 25 (1974), pp. 155--188.
Mathematical Reviews (MathSciNet): MR505430
Digital Object Identifier: doi:10.1093/bjps/27.1.25

2009 © Duke University Press