The Infinite Variety of Logics

Every knowledge representation language is a thinly disguised version of logic, often with a specialized ontology built into the notation. The number of possible notations for pure logic and the number of ontologies that could be combined with them are infinite. No single notation can ever be ideal for all possible applications, and new ones will always be found that can help to simplify various kinds of problems. Fortunately, the great diversity of logics can all be related to one another through a relatively small number of fundamental principles. This paper presents some examples that illustrate the advantages of different representation and the methods of mapping one to another.

[1]  R. Jeffrey,et al.  The Philosophy of Rudolf Carnap , 1966 .

[2]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[3]  Bernhard Nebel,et al.  KI-97: Advances in Artificial Intelligence , 1997, Lecture Notes in Computer Science.

[4]  Marvin Minsky,et al.  Semantic Information Processing , 1968 .

[5]  Drew McDermott,et al.  Nonmonotonic Logic and Temporal Projection , 1987, Artif. Intell..

[6]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[7]  Edward R. Tufte.  Visual explanations: images and quantities, evidence and narrative , 1997 .

[8]  Richard Fikes,et al.  STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving , 1971, IJCAI.

[9]  Peter Grünwald,et al.  Causation and Nonmonotonic Temporal Reasoning , 1997, KI.

[10]  Evert W. Beth,et al.  Semantic Entailment And Formal Derivability , 1955 .

[11]  D. Roberts.  The existential graphs , 1992 .

[12]  H. Kamp,et al.  Evénements, représentations discursives et référence temporelle , 1981 .

[13]  John F. Sowa,et al.  Conceptual Structures: Information Processing in Mind and Machine , 1983 .

[14]  C. Peirce.  On the Algebra of Logic: A Contribution to the Philosophy of Notation , 1885 .

[15]  J. McCarthy.  Situations, Actions, and Causal Laws , 1963 .

[16]  G. Gentzen.  Untersuchungen über das logische Schließen. I , 1935 .

[17]  Chuck Rieger,et al.  An Organization of Knowledge for Problem Solving and Language Comprehension , 1976, Artif. Intell..

[18]  A. Troelstra.  Lectures on linear logic , 1992 .

[19]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.