Hybrid Logic And Its Proof Theory

Hybrid Logic and its Proof-Theory

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Computer Science Research Report

Theoretical Information Reuse and Integration

Information Reuse and Integration addresses the efficient extension and creation of knowledge through the exploitation of Kolmogorov complexity in the extraction and application of domain symmetry. Knowledge, which seems to be novel, can more often than not be recast as the image of a sequence of transformations, which yield symmetric knowledge. When the size of those transformations and/or the length of that sequence of transforms exceeds the size of the image, then that image is said to be novel or random. It may also be that the new knowledge is random in that no such sequence of transforms, which produces it exists, or is at least known. The nine chapters comprising this volume incorporate symmetry, reuse, and integration as overt operational procedures or as operations built into the formal representations of data and operators employed. Either way, the aforementioned theoretical underpinnings of information reuse and integration are supported.