A new class of program-oriented logical formalisms is investigated – renominative logics with extended renominations, equality predicates, and predicate complement composition. Composition algebras and languages of such logics are described; their semantic properties are investigated. For these logics, a number of logical consequence relations are proposed and investigated, in particular, the logical consequence relations with undefinedness conditions. Properties of these relations form the semantic basis for further construction of sequent-type calculi for the proposed logics.

The problem of representing a single localized particle has played a crucial role in the historical development of quantum theories. In particular, the failure to construct a relativistically invariant position eigenstate was a contributing factor in the demise of the so-called relativistic quantum mechanics, in favor of quantum field theories. Nevertheless, non-locality which stems from standard accounts of Single-particle localization still presents itself as a problem in the form of Gerhard Hegerfeldt's eponymous theorem of 1974. Accepting that a link may (...) be maintained between invariance and 'objectivity,' it is shown how Hegerfeldt's paradoxical result arises in relativistic theories from a failure of objectivity of localization-the so-called 'Jericho effect'. (shrink)