By Lakatos I., Musgrave A. (eds.)

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Extra resources for Problems in the philosophy of science: Proceedings London, 1965

Example text

Stalnaker and G. Pearce. (1981) Ifs. Reidel, Dordrecht, 1981. [Hintikka,1962] 1. Hintikka. Knowledge and Belief Cornell University Press, Ithaca, NY, 1962. [Hughes and Cresswell, 1968] G. E. Hughes and M. 1. Cresswell. An Introduction to Modal Logic. Methuem, London, 1968. [Rescher, 1969] N. Rescher. Many-valuedLogics. McGraw-Hill, 1969. [Voorbraak,1993] F. As Far as I Know: Epistemic Logic and Uncertainty. Dissertation, Utrecht University, 1993. Dynamic of Belief [Giirdenfors,1988] P. Giirdenfors.

It is less resourceconsuming than floating-point addition, but it is subject to overflow. As the overflow generally results in a disaster, one may try to limit the damages by always chopping addition to the maximum number expressible (2 32 - 1, or 2 64 - 1). 1 Bochvar's and Kleene's systems Bochvar's and Kleene's are both three-valued systems. In addition to 0 and 1 for false and true, they have a third value 2. While for Lukasiewicz the third value stands for possible, or not yet detennined, from Bochvar's point of view it stands for paradoxical, or meaningless.

Choose a subalgebra S ofP( M); S will constitute the set of signs of our tableau calculus. For any S E S and any connective c, one constructs an Sth DNF for c, meaning a signed formula expression of the form C 1 V·· ·VCh, where each C. is a conjunct of signed formulas from the set {p; : 1 ::; r ::; u, T E S}. The condition to be fulfilled is that, for any (J', (J' satisfies (CP1 ... Pu)S iff there exists s such that (J' satisfies all the signed formulas in Cs. As before, C 1 V ... V Ch induces a tableau elimination rule for c at place S.