Introduction to higher order categorical logic
Introduction to higher order categorical logic
A framework for intuitionistic modal logics
Proceedings of the 1986 Conference on Theoretical aspects of reasoning about knowledge
Notions of computation and monads
Information and Computation
A modal analysis of staged computation
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Information and Computation
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Explicit Substitutions for Constructive Necessity
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A judgmental reconstruction of modal logic
Mathematical Structures in Computer Science
Computational types from a logical perspective
Journal of Functional Programming
Embedding Constructive K into Intuitionistic K
Electronic Notes in Theoretical Computer Science (ENTCS)
An intuitionistic epistemic logic for sequential consistency on shared memory
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Cut-free Gentzen calculus for multimodal CK
Information and Computation
Constructive linear-time temporal logic: Proof systems and Kripke semantics
Information and Computation
A categorical outlook on relational modalities and simulations
Information and Computation
Countermodels from Sequent Calculi in Multi-Modal Logics
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Cut elimination in nested sequents for intuitionistic modal logics
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
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We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics.