CS245 Study Guide - Logical Consequence, Uch, Soundness
Document Summary
The alphabet for modal (propositional) logic is the same as for propositional logic with the addition of an additional unary connectives 2 (called necessarily or always) and 3 (called possibly or eventually). In the following we assume that is a shorthand for ( ) , for ( ( )), and. Let p be a set of propositional symbols. The pair (w, r) is called the frame of i. A pair (i, w) such that i, w |= is called a (pointed) model of . We de ne mod( ) to be the mod( ) = {(i, w) | (i, w) |= }. Note: in many presentations the term model and interpretation are used as synonyms; such a termi- nology, however, makes de ning validity, satis ability, and logical implication cumbersome. De nitions of logical implication ( |= ) and equivalence, and their properties are now the same as for propositional logic.
