Although classical first-order logic is the de facto standard logical foundation for artificial intelligence, the lack of a built-in, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems.
Let me here mention that closely associated with this dilemma are two related traditions, one attempting to work out a logic for imperatives, the other rejecting the prospect for a logic of imperatives, but stressing the importance of imperatives as semantic components in devising a logical foundation for normative propositions.
Unlike the other seminal papers in nonmonotonic logic, Reiter's shows specific influence from the earlier and independent work on nonmonotonicity in logic programming the work seems to have been largely inspired by the need to provide logical foundations for the nonmonotonic reasoning found in deductive databases.
Similarly, discrete mathematics and logic are foundations for computer based disciplines such as computer science, software engineering and information systems.
In recent decades, Dr. Hinton, 64 (a great-great-grandson of the 19th-century mathematician George Boole, whose work in logic is the foundation for modern digital computers), has pioneered powerful new techniques for helping the artificial networks recognize patterns.
From this point of view Brentano appears as one of the last advocates of the "old logic", and his theory as a final attempt at providing a psychological foundation for logic.
The latter are construed as constituting an ontological foundation for logic, and hence for mathematics (pursuant to Frege's logicist program).
Because a digital logic course lays the foundation for other courses, such as courses on computer organization and architecture, early exposure to PDC concepts will have a wide reach.
OWL is based on an expressive, decidable fragment of first-order logic and provides the foundation for the Semantic Web.
The idea of possible worlds raised the prospect of extensional respectability for modal logic, not by rendering modal logic itself extensional, but by endowing it with an extensional semantic theory — one whose own logical foundation is that of classical predicate logic and, hence, one on which possibility and necessity can ultimately be understood along classical Tarskian lines.
