The current paper details a restricted semantics for active logic, a time-sensitive, contradictiontolerant logical reasoning formalism. Central to active logic are special rules controlling the inheritance of beliefs in general, and beliefs about the current time in particular, very tight controls on what can be derived from direct contradictions (P&¬P ), and mechanisms allowing an agent to rep...

For some time we have been developing, and have had significant practical success with, a time-sensitive, contradiction-tolerant logical reasoning engine called the active logic machine (ALMA). The current paper details a semantics for a version of the underlying logical formalism, active logic. Central to active logic are special rules controlling the inheritance of beliefs in general (and of ...

Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language befor...

The article studies common knowledge in communication networks with a fixed topological structure. It introduces a non-trivial principle, called the Ryōan-ji axiom, which captures logical properties of common knowledge of all protocols with a given network topology. A logical system, consisting of the Ryōan-ji axiom and two additional axioms, is proven to be sound and complete.