The aim of this work is to implement temporal logic in the Coq proof assistant system. This implementation uses the logical language of Coq as meta-language for temporal logic representation. The work starts with a crash introduction to Coq devoted to introduce the Coq system. The implementation of linear temporal logic and two branching temporal logics is discussed. In both linear and branching temporal logic soundness verification of proposed axiomatizations is made. Some application examples are shown. 1 Acknowledgments To Prof. Am'ilcar Sernadas, whitout whom this work would not have been possible, for his ideas and guidance. To Carlos for his guidance, constant help, presence and friendship. To Jaime and Paulo for their suggestions. To Sara and Alexandra for their good humor, support and fellowship. To all section 84. This work was partially supported by the PRAXIS XXI Program and FCT, as well as by PRAXIS XXI Projects 2/2.1/MAT/262/94 SitCalc, PCEX/P/MAT/46/96 ACL plus 2/2.1/TI...

The main goal of this work is to implement some versions of the Situation Calculus in Coq. This is done through various stages. First we implement the Situation and State Calculus, then the Linear Situation and State Calculus and finally the Object Situation and State Calculus. In addition we verify the soundness, with respect to standard interpretation structures, of the proposed axiomatizations. Finally we are able to specify and verify systems. 1 Acknowledgments To Prof. Am'ilcar Sernadas, my supervisor, for offering me the opportunity to do this work, for his motivation and many suggestions. To Jaime for his patience and generous help which were invaluable. To Carlos and Paulo for their suggestions and positive presence. To Alexandra and Nuno for their companionship and constant support. My thanks also go to all section 84. This work was partially supported by the PRAXIS XXI Program and FCT, as well as by PRAXIS XXI Projects 2/2.1/MAT/262/94 SitCalc, PCEX/P/MAT/46/96 ACL pl...