Discrete Linear Temporal Logic with Knowing-Value Operator

Abstract

In epistemic logic we are not only interested in the propositional knowledge expressed by “knowing that” operators, but also care about other types of knowledge used in natural language. In [1], Plaza proposed the “knowing value” operators and gave the complete axiomatization for the logic of knowledge with nonrigid designators. Moreover, in [2] Halpern and colleagues holds that, when analyzing a system in terms of knowledge, not only is the current state of knowledge of the agents in the system relevant, but also how that state of knowledge changes over time. So we introduce temporal logic operators ‘next’ and ‘until’ to extend Plaza’s system. The completeness proof is highly non-trivial and we referred to the work of [2, 3].