Axiomatic Systems and Topological Semantics for Intuitionistic Temporal Logic [chapter]

Joseph Boudou, Martín Diéguez, David Fernández-Duque, Fabián Romero
2019 Lecture Notes in Computer Science  
0000−0003−3440−4348] , David Fernández-Duque 3[0000−0001−8604−4183] , and Fabián Romero 1[0000−0003−1242−5391] Abstract. The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional languages with new features via type theory, while from its semantical perspective several logics for reasoning about
more » ... dynamical systems and several semantics for logic programming have their roots in this framework. In this paper we propose four axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. Our topological semantics features a new interpretation for the 'henceforth' modality that is a natural intuitionistic variant of the classical one. Using the soundness results, we show that the four logics obtained from the axiomatic systems are distinct. Martín Diéguez is funded by the ANR-12-ASTR-0020 project STRATEGIC and the European COST Action CA17124. 4 Staged computation is a technique that allows dividing the computation in order to exploit the early availability of some arguments.
doi:10.1007/978-3-030-19570-0_49 fatcat:bsx7jvjd6jhnbi2m3ir5yofagy