We propose a logical formalisation of computational errors in reactive, nondeterministic systems. To this aim, we introduce a new three-valued symmetric nondeterministic disjunction, designed to provide a faithful logical representation of the nondeterministic choice arising in concurrent computations. The connective is defined within the framework of nondeterministic matrices (Nmatrices) and derives from a minimal combination of Kleene's tolerant semantics and Bochvar's symmetric error persistence, thereby eliminating the residual asymmetry induced by sequential evaluation strategies such as McCarthy's logic. The resulting semantics admits genuinely nondeterministic outcomes in mixed cases involving errors, while preserving commutativity and operational symmetry.
A Logical 3-valued Semantics for Nondeterministic Choice
Alessandro Aldini
;Pierluigi Graziani;Claudio Antares Mezzina;Gandolfo Vergottini
2026
Abstract
We propose a logical formalisation of computational errors in reactive, nondeterministic systems. To this aim, we introduce a new three-valued symmetric nondeterministic disjunction, designed to provide a faithful logical representation of the nondeterministic choice arising in concurrent computations. The connective is defined within the framework of nondeterministic matrices (Nmatrices) and derives from a minimal combination of Kleene's tolerant semantics and Bochvar's symmetric error persistence, thereby eliminating the residual asymmetry induced by sequential evaluation strategies such as McCarthy's logic. The resulting semantics admits genuinely nondeterministic outcomes in mixed cases involving errors, while preserving commutativity and operational symmetry.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
