Propositional Logic
Propositional logic is "classical" logic from which the quantifiers
have been excluded. There is a unary negation operator and standard
connectives are used: conjunction, disjunction and implication. The
only way to say that, "Every dog has a tail," is to write a long
series of axioms, one for each element in the universe. For a
specific such element E, the axiom associated with E would say that if
E is a dog, then E has a tail.
Determining whether or not a propositional theory is consistent ("has
a model", in slightly more technical terms) is NP-complete. This
means that if the theory is consistent as demonstrated by a specific
assignment of true or false to each sentence, validating that
assignment is straightforward. There are no known efficient
algorithms for producing the assignment, although it is not known that
such algorithms do not exist.
CIRL
Propositional logic plays a central role in much of
CIRL's work. Although its representational inefficiencies generally
make it unsuited for fielded applications, its clean syntax and
semantics make it an ideal domain in which to develop new algorithms
and explore their behavior.
Parent areas:
Language
Subareas:
Quantified propositional logic
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