Intuitionistic Linear Temporal Logics
This work addresses foundational issues in temporal logic for formal verification and AI, but it is incremental as it builds on existing intuitionistic and temporal logic frameworks.
The paper tackles the problem of defining and analyzing intuitionistic variants of linear temporal logic based on expanding posets, proving that one variant (ILTL) is decidable with the effective finite model property, while another (ITLB) lacks the finite model property, and showing that 'until' and 'release' operators are not mutually definable over persistent posets.
We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic which we denote $\iltl$, and by imposing additional constraints we obtain the logics $\itlb$ of persistent posets and $\itlht$ of here-and-there temporal logic, both of which have been considered in the literature. We prove that $\iltl$ has the effective finite model property and hence is decidable, while $\itlb$ does not have the finite model property. We also introduce notions of bounded bisimulations for these logics and use them to show that the `until' and `release' operators are not definable in terms of each other, even over the class of persistent posets.