This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Semantic analysis, – inference on the basis of semantic information and world knowledge – still is largely uncharted territory in dy- (3) namic semantics. It is needed, among other things, for the reconstruction of linguistically unspecified parts of the discourse or for restricting ambiguities introduced by prior analysis processes, i.e.

These notes discuss formalizing contexts as first class objects. The basic relationships are: ist(c,p) meaning that the proposition p is true in the context c, and value(c,p) designating the value of the term e in the context c Besides these, there are lifting formulas that relate the propositions and terms in subcontexts to possibly more general propositions and terms in the outer context. Subcontextx are often specialised with regard to time, place and terminology. Introducing contexts as formal objects will permit (...) axiomatizations in limited contexts to be expanded to transcend the original limitations. This seems necessary to provide AI programs using logic with certain capabilities that human fact representation and human reasoning possess. Fully implementing transcendence seems to require further extensions to mathematical logic, ie. beyond the nonmonotonic inference methods first invented in AI and now studied as a new domain of logic. (shrink)