Bisimulation and Propositional Intuitionistic Logic

The Brouwer-Heyting-Kolmogorov interpretation of intuitionistic logic suggests that p⊃q can be interpreted as a computation that given a proof of p constructs a proof of q. Dually, we show that every finite canonical model of q contains a finite canonical model of p. If q and p are interderivable, their canonical models contain each other.

[1]  M. Fitting Intuitionistic logic, model theory and forcing , 1969 .

[2]  Fabio Bellissima,et al.  Finitely generated free Heyting algebras , 1986, Journal of Symbolic Logic.

[3]  J. Davenport Editor , 1960 .

[4]  A. Tarski,et al.  On Closed Elements in Closure Algebras , 1946 .

[5]  R. Sikorski,et al.  The mathematics of metamathematics , 1963 .

[6]  A. Tarski,et al.  The Algebra of Topology , 1944 .

[7]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[8]  K. Gödel,et al.  Kurt Gödel : collected works , 1986 .

[9]  Peter Aczel,et al.  Non-well-founded sets , 1988, CSLI lecture notes series.

[10]  J.F.A.K. van Benthem,et al.  Modal Correspondence Theory , 1977 .

[11]  M. de Rijke,et al.  Modal Logic and Process Algebra , 1995 .

[12]  M. Hollenberg Hennessy-Milner Classes and Process Algebra , 1994 .

[13]  R. Goldblatt Mathematics of modality , 1993 .

[14]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[15]  Iwao Nishimura,et al.  On Formulas of One Variable in Intuitionistic Propositional Calculus , 1960, J. Symb. Log..

[16]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[17]  A. Heyting,et al.  Intuitionism: An introduction , 1956 .

[18]  Saul A. Kripke,et al.  Semantical Analysis of Intuitionistic Logic I , 1965 .

[19]  J. C. C. McKinsey,et al.  A Solution of the Decision Problem for the Lewis systems S2 and S4, with an Application to Topology , 1941, J. Symb. Log..

[20]  H. Gaifman,et al.  Symbolic Logic , 1881, Nature.