Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q+, ,D, where Q+ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q+, Dv and if v w, then D v . D v D w . Moreover, simple completeness proofs of extensions of Q-LC are given.

A system of modal logic with the operator is proposed, and proved complete. In contrast with a previous one by Stalnaker and Thomason, this system does not require two categories of singular terms.

This volume is about abstract objects and the ways we refer to them in natural language. Asher develops a semantical and metaphysical analysis of these entities in two stages. The first reflects the rich ontology of abstract objects necessitated by the forms of language in which we think and speak. A second level of analysis maps the ontology of natural language metaphysics onto a sparser domain--a more systematic realm of abstract objects that are fully analyzed. This second level reflects the (...) commitments of real metaphysics. The models for these commitments assign truth conditions to natural language discourse. Annotation copyright by Book News, Inc., Portland, OR. (shrink)

The aims of this paper are: (1) to present tense-logical versions of such classical notions as saturated and special models; (2) to establish several fundamental existence theorems about these notions; (3) to apply these powerful techniques to tense complexity.In this paper we are concerned exclusively with quantifiedK 1 (for linear time) with constant domain. Our present research owes much to Bowen [2], Fine [5] and Gabbay [6].

It is shown that the expressive power of second-order propositional modal logic whose modalities are S4.2 or weaker is the same as that of second-order predicate logic.

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme □∃xφ ⊃ ∃x□φ.

This paper is about two puzzles, or two versions of a single puzzle, which deserve to be called paradoxes, and develops some apparatus in terms of which the apparently conflicting principles which generate the puzzles can be rendered consistent. However, the apparatus itself is somewhat controversial: the puzzles are modal ones, and the resolution to be advocated requires the adoption of a counterpart theoretic semantics of essentially the kind proposed by David Lewis, which in turn requires qualified rejection of certain (...) modal theses about identity which are valid in S5. (shrink)

The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).

This paper is part of a general programme of developing and investigating particular first- order modal theories. In the paper, a modal theory of propositions is constructed under the assumption that there are genuinely singular propositions, ie. ones that contain individuals as constituents. Various results on decidability, axiomatizability and definability are established.