Probabilistic and quantum institutions revisited

We revisit quantum institutions as in [2] and solve some problems identified therein. Global, probabilistic and quantum exogenous enrichments of logics are adapted to a new notion of global model. For simplicity sake, all the constructions are presented in the realm of satisfaction systems, which proves to be an appropriate framework for defining the new logics. It also provides suitable constructions for studying the relationship between these enrichments and compare them with the constructions of [2]. Nevertheless, all the constructions are shown to be easily extended to institutions.

[1]  Rohit Chadha,et al.  Reasoning About Imperative Quantum Programs , 2006, MFPS.

[2]  P. Mateus,et al.  Exogenous Quantum Logic , 2004 .

[3]  Amílcar Sernadas,et al.  Weakly complete axiomatization of exogenous quantum propositional logic , 2005, Inf. Comput..

[4]  Nils J. Nilsson,et al.  Probabilistic Logic Revisited , 1993, Artif. Intell..

[5]  Roberto Giuntini,et al.  Reasoning in quantum theory , 2004 .

[6]  Joseph A. Goguen,et al.  Some Fundamental Algebraic Tools for the Semantics of Computation. Part II: Signed and Abstract Theories , 1984, Theor. Comput. Sci..

[7]  H. Dishkant,et al.  Logic of Quantum Mechanics , 1976 .

[8]  J. Neumann,et al.  The Logic of Quantum Mechanics , 1936 .

[9]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[10]  Joseph A. Goguen,et al.  Some Fundamental Algebraic Tools for the Semantics of Computation: Part 3: Indexed Categories , 1991, Theor. Comput. Sci..

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

[12]  Joseph A. Goguen,et al.  Some Fundamental Algebraic Tools for the Semantics of Computation. Part 1: Comma Categories, Colimits, Signatures and Theories , 1984, Theor. Comput. Sci..

[13]  Joseph A. Goguen,et al.  A Study in the Functions of Programming Methodology: Specifications, Institutions, Charters and Parchments , 1985, CTCS.

[14]  David J. Foulis,et al.  A Half-Century of Quantum Logic What Have We Learned? , 1999 .

[15]  Gai CarSO.  A Logic for Reasoning about Probabilities * , 2004 .

[16]  Rohit Chadha,et al.  Reasoning About States of Probabilistic Sequential Programs , 2006, CSL.

[17]  José Meseguer,et al.  General Logics , 2006 .

[18]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[19]  Cristina Sernadas,et al.  Quantum Institutions , 2006, Essays Dedicated to Joseph A. Goguen.

[20]  Grigore Rosu,et al.  Institution Morphisms , 2013, Formal Aspects of Computing.

[21]  P. Mateus,et al.  Exogenous Semantics Approach to Enriching Logics , 2005 .

[22]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[23]  Amílcar Sernadas,et al.  Reasoning About Quantum Systems , 2004, JELIA.