A uniform quantificational logic for algebraic notions ofcontext
Year: 2002
Type: book
Abstract: A quantificational framework of formal reasoning is proposed, which emphasises the pattern\nof entering and exiting context. Contexts are modelled by an algebraic structure which reflects\nthe order and manner in which context is entered into and exited from.\nThe equations of the algebra partitions context terms into equivalence classes. A formal\nsemantics is defined, containing models that map equivalence classes of certain context terms\nto sets of first order structures.\nThe corresponding Hilbert system incorporates the algebraic equations as axioms asserted in\ncontext. In this way a uniform logic for arbitrary algebras of context is obtained. Soundness\nand completeness are proved.\nIn semigroups of contexts, where combination of contexts is associative, finite ground\nalgebraic equations correspond to contingent equivalence between certain logical formulas.\nSystems for sets and multisets of contexts are obtained by presenting their respective algebras\nas associativity plus finite ground equations.\nSome contextual reasoning systems in the literature are inherently associative, and we present\nthose as special cases.
Author: Rolf Nossum
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2467470178