The modal logician's notion of possible world and the computer scientist's notion of state of a machine provide a point of commonality which can form the foundation of a logic of action. Extending ordinary modal logic with the calculus of binary relations leads to a very natural logic for describing the behavior of computer programs.
Members of the Ba2Zn1-xCdxTa2O9 (0 =< x =< 1) series have been synthesized by solid state reactions at 1473 K. Powder x-ray diffraction studies show a cubic perovskite cell with a ~ 4.1 a which increases with increase in x. Electron diffraction studies show the presence of hexagonal ordered perovskite structure in addition to the cubic structure seen by x-rays, the x = 0.5 composition showing more ordered crystallites. (...) These samples show high dielectric constants with a maximum (r = 30 at 1 kHz) for the x = 0.5 member. The dielectric loss increases with increase in x at all the frequencies under study. (shrink)
Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result (...) is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of prepositional dynamic logic, and yet another notion of regular algebra. (shrink)
The approach to critical realism, by D. Drake.--Pragmatism versus the pragmatist, by A. O. Lovejoy.--Critical realism and the possibility of knowledge, by J. B. Pratt.--The problem of error, by A. K. Rogers.--Three proofs of realism, by G. Santayana.--Knowledge and its categories, by R. W. Sellars.--On the nature of the datum, by C. A. Strong.
The people and the value of their experience, by N. T. Pratt.--From kingship to democracy, by J. P. Harland.--Democracy at Athens, by G. M. Harper.--Athens and the Delian League, by B. D. Meritt.--Socialism at Sparta, by P. R. Coleman-Norton.--Tyranny, by M. Mac Laren.--Federal unions, by C. A. Robinson.--Alexander and the world state, by O. W. Reinmuth.--The Antigonids, by J. V. A. Fine.--Ptolemaic Egypt: a planned economy, by S. L. Wallace.--The Seleucids: the theory of monarchy, by G. Downey.--The political status (...) of the independent cities of Asia Minor in the Hellenistic period, by D. Magie.--The ideal states of Plato and Aristotle, by W. J. Oates.--Epilogue, by A. C. Johnson.--Bibliography (p. 225-233).--Index, by H. V. M. Dennis, III. (shrink)
A region-based model of physical space is one in which the primitive spatial entities are regions, rather than points, and in which the primitive spatial relations take regions, rather than points, as their relata. Historically, the most intensively investigated region-based models are those whose primitive relations are topological in character; and the study of the topology of physical space from a region-based perspective has come to be called mereotopology. This paper concentrates on a mereotopological formalism originally introduced by Whitehead, (...) which employs a single primitive binary relation C(x,y) (read: x is in contact with y). Thus, in this formalism, all topological facts supervene on facts about contact. Because of its potential application to theories of qualitative spatial reasoning, Whitehead's primitive has recently been the subject of scrutiny from within the Artificial Intelligence community. Various results regarding the mereotopology of the Euclidean plane have been obtained, settling such issues as expressive power, axiomatization and the existence of alternative models. The contribution of the present paper is to extend some of these results to the mereotopology of three-dimensional Euclidean space. Specifically, we show that, in a first-order setting where variables range over tame subsets of R 3, Whitehead's primitive is maximally expressive for topological relations; and we deduce a corollary constraining the possible region-based models of the space we inhabit. (shrink)