A uniform quantificational logic for algebraic notions ofcontext
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http://hdl.handle.net/11250/135043Utgivelsesdato
2002Metadata
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- Publication Series [82]
Sammendrag
A quantificational framework of formal reasoning is proposed, which emphasises the pattern
of entering and exiting context. Contexts are modelled by an algebraic structure which reflects
the order and manner in which context is entered into and exited from.
The equations of the algebra partitions context terms into equivalence classes. A formal
semantics is defined, containing models that map equivalence classes of certain context terms
to sets of first order structures.
The corresponding Hilbert system incorporates the algebraic equations as axioms asserted in
context. In this way a uniform logic for arbitrary algebras of context is obtained. Soundness
and completeness are proved.
In semigroups of contexts, where combination of contexts is associative, finite ground
algebraic equations correspond to contingent equivalence between certain logical formulas.
Systems for sets and multisets of contexts are obtained by presenting their respective algebras
as associativity plus finite ground equations.
Some contextual reasoning systems in the literature are inherently associative, and we present
those as special cases.
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