22,529 research outputs found
A Note on Parameterised Knowledge Operations in Temporal Logic
We consider modeling the conception of knowledge in terms of temporal logic.
The study of knowledge logical operations is originated around 1962 by
representation of knowledge and belief using modalities. Nowadays, it is very
good established area. However, we would like to look to it from a bit another
point of view, our paper models knowledge in terms of linear temporal logic
with {\em past}. We consider various versions of logical knowledge operations
which may be defined in this framework. Technically, semantics, language and
temporal knowledge logics based on our approach are constructed. Deciding
algorithms are suggested, unification in terms of this approach is commented.
This paper does not offer strong new technical outputs, instead we suggest new
approach to conception of knowledge (in terms of time).Comment: 10 page
The Logic behind Feynman's Paths
The classical notions of continuity and mechanical causality are left in
order to refor- mulate the Quantum Theory starting from two principles: I) the
intrinsic randomness of quantum process at microphysical level, II) the
projective representations of sym- metries of the system. The second principle
determines the geometry and then a new logic for describing the history of
events (Feynman's paths) that modifies the rules of classical probabilistic
calculus. The notion of classical trajectory is replaced by a history of
spontaneous, random an discontinuous events. So the theory is reduced to
determin- ing the probability distribution for such histories according with
the symmetries of the system. The representation of the logic in terms of
amplitudes leads to Feynman rules and, alternatively, its representation in
terms of projectors results in the Schwinger trace formula.Comment: 15 pages, contribution to Mario Castagnino Festschrif
Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy
We present a model of set theory, in which, for a given , there exists
a non-ROD-uniformizable planar lightface set in , whose all vertical cross-sections are countable sets (and in
fact Vitali classes), while all planar boldface sets with
countable cross-sections are -uniformizable. Thus it is true
in this model, that the ROD-uniformization principle for sets with countable
cross-sections first fails precisely at a given projective level.Comment: A revised version of the originally submitted preprin
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