Free Logic in Program Specification and Verification

This paper illustrates important applications of free logic in computer science. In computer science there is a strong interest in formalizing appropriate theories, and free logic is well-suited for these applications1.

[1]  Karel Lambert,et al.  Existential import revisited , 1963, Notre Dame J. Formal Log..

[2]  Jaako Hintikka,et al.  Existential Presuppositions and Existential Commitments , 1959 .

[3]  D. Scott,et al.  Sheaves and logic , 1979 .

[4]  H. Keisler,et al.  Handbook of mathematical logic , 1977 .

[5]  Karel Lambert,et al.  Universally free logic and standard quantification theory , 1968, Journal of Symbolic Logic.

[6]  Karel Lambert,et al.  On Free Description Theory , 1967 .

[7]  Karel Lambert,et al.  Derivation and Counterexample: An Introduction to Philosophical Logic , 1972 .

[8]  Dana S. Scott,et al.  Existence and Description in Formal Logic , 1973 .

[9]  Bertrand Russell,et al.  Bertrand Russell: Philosopher of the Century , 1967 .

[10]  Hugues Leblanc Existence, truth, and provability , 1980 .

[11]  Raymond D. Gumb Programming logics - an introduction to verification and semantics , 1989 .

[12]  Hugues Leblanc Truth-Value Semantics , 1976 .

[13]  Henry S. Leonard,et al.  The logic of existence , 1956 .

[14]  Erich J. Neuhold,et al.  Formal description of programming concepts , 1991 .

[15]  C. A. R. Hoare,et al.  An axiomatic basis for computer programming , 1969, CACM.

[16]  Hugues Leblanc,et al.  Nondesignating singular terms , 1959 .

[17]  Karel Lambert,et al.  Free logic and the concept of existence , 1967, Notre Dame J. Formal Log..

[18]  R. D. Tennent,et al.  A Note on Undefined Expression Values in Programming Logics , 1987, Inf. Process. Lett..

[19]  Carl J. Posy A free IPC is a natural logic: Strong completeness for some intuitionistic free logics , 1982 .

[20]  Karel Lambert Philosophical applications of free logic , 1991 .

[21]  D. Scott Identity and existence in intuitionistic logic , 1979 .

[22]  D. Scott,et al.  Applications of sheaves , 1979 .

[23]  Joseph A. Goguen,et al.  Abstract Errors for Abstract Data Types , 1977, Formal Description of Programming Concepts.

[24]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[25]  Robert L. Constable,et al.  Partial Objects In Constructive Type Theory , 1987, Logic in Computer Science.

[26]  M. Fourman The Logic of Topoi , 1977 .

[27]  Karel Lambert On the Philosophical foundations of free description theory , 1987 .

[28]  Karel Lambert,et al.  Notes on E! III: A theory of descriptions , 1962 .

[29]  Bjørn Kirkerud,et al.  Completeness of hoare-calculi revisited , 1982, BIT.