Dynamic algebras: Examples, constructions, applications

DOI10.1007/BF00370685zbMath0752.03033OpenAlexW2022554132MaRDI QIDQ1189900

Vaughan R. Pratt

Publication date: 27 September 1992

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00370685

zbMATH Keywords

Boolean algebraregular algebrafree dynamic algebras

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Logic in computer science (03B70) Logical aspects of Boolean algebras (03G05) Boolean algebras with additional operations (diagonalizable algebras, etc.) (06E25)

Related Items (27)

Algebras of modal operators and partial correctness ⋮ Concurrent Dynamic Algebra ⋮ Linear and affine logics with temporal, spatial and epistemic operators ⋮ On dynamic algebras ⋮ Canonical finite models of Kleene algebra with tests ⋮ Some modal aspects of XPath ⋮ Algebraic Semantics for Dynamic Dynamic Logic ⋮ Congruences and ideals on Peirce algebras: a heterogeneous/homogeneous point of view ⋮ Boolean-like algebras ⋮ Complexity of equations valid in algebras of relations. I: Strong non-finitizability ⋮ Algebraic notions of nontermination: Omega and divergence in idempotent semirings ⋮ Non-termination in Idempotent Semirings ⋮ Axiomatizability of representable domain algebras ⋮ On the equational definition of the least prefixed point. ⋮ On the complexity of Kleene algebra with domain ⋮ Epistemic Logics of Structured Intensional Groups ⋮ Dynamic Łukasiewicz logic and dynamic MV-algebras ⋮ On the dynamic logic of agency and action ⋮ Every free algebra in the variety generated by the representable dynamic algebras is separable and representable ⋮ The equational theory of Kleene lattices ⋮ MacNeille completions and canonical extensions ⋮ Complete axiomatizations for XPath fragments ⋮ Completion of Boolean algebras in MSet ⋮ Equational theories for automata ⋮ A proof system for contact relation algebras ⋮ Unnamed Item ⋮ PDL has interpolation

Cites Work

• Dynamic algebras with test
• A near-optimal method for reasoning about action
• Complexity of Boolean algebras
• A calculus of communicating systems
• Application of modal logic to programming
• Boolean modules
• Every free algebra in the variety generated by the representable dynamic algebras is separable and representable
• Propositional dynamic logic of regular programs
• A completeness theorem for Kleene algebras and the algebra of regular events
• On representable relation algebras
• Temporal Structures
• The Logic of Equality
• Two Complete Axiom Systems for the Algebra of Regular Events
• An axiomatic basis for computer programming
• Heterogeneous algebras
• The Theory of Representation for Boolean Algebras
• On the calculus of relations
• On sentences which are true of direct unions of algebras
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