Specification-oriented semantics for communicating processes
Acta Informatica
Proceedings of the international conference on Mathematical foundations of programming semantics
Galois connections and computer science applications
Proceedings of a tutorial and workshop on Category theory and computer programming
Topology via logic
On the shape of mathematical arguments
On the shape of mathematical arguments
Handbook of theoretical computer science (vol. B)
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Handbook of logic in computer science (vol. 2)
Science of Computer Programming - Special issue on mathematics of program construction
Information Processing Letters - Special issue on the calculational method
Lagois connections: a counterpart to Galois connections
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics. Part II : lambda calculus and domain theory: lambda calculus and domain theory
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
The temporal logic of coalgebras via Galois algebras
Mathematical Structures in Computer Science
A note on coalgebras and presheaves
Mathematical Structures in Computer Science
Algebras of modal operators and partial correctness
Theoretical Computer Science - Algebraic methodology and software technology
Automated Reasoning in Kleene Algebra
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Logics from Galois connections
International Journal of Approximate Reasoning
Context Algebras, Context Frames, and Their Discrete Duality
Transactions on Rough Sets IX
Positive Logic with Adjoint Modalities: Proof Theory, Semantics and Reasoning about Information
Electronic Notes in Theoretical Computer Science (ENTCS)
Making Temporal Logic Calculational: A Tool for Unification and Discovery
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Pointfree expression and calculation: from quantification to temporal logic
Formal Methods in System Design
Learning in a changing world, an algebraic modal logical approach
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
Studia Logica
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We develop temporal logic from the theory of complete lattices, Galois connections and fixed points. In particular, we prove that all seventeen axioms of Manna and Pnueli's sound and complete proof system for linear temporal logic can be derived from just two postulates, namely that (⊕, &⊖tilde;) is a Galois connection and that (⊖, ⊕) is a perfect Galois connection. We also obtain a similar result for the branching time logic CTL.A surprising insight is that most of the theory can be developed without the use of negation. In effect, we are studying intuitionistic temporal logic. Several examples of such structures occurring in computer science are given. Finally, we show temporal algebra at work in the derivation of a simple graph-theoretic algorithm.This paper is tutorial in style and there are no difficult technical results. To the experts in temporal logics, we hope to convey the simplicity and beauty of algebraic reasoning as opposed to the machine-orientedness of logical deduction. To those familiar with the calculational approach to programming, we want to show that their methods extend easily and smoothly to temporal reasoning. For anybody else, this text may serve as a gentle introduction to both areas.