
Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation2 in a compositional fashion. For example, No whale flies is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on semantic knowledge. For …Read more

On semilattice relevant logicsMathematical Logic Quarterly 49 (4): 401. 2003.The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cutfree labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbertstyle axiomatizations for ∪R and ∪T and prove equivalence between t…Read more

Sequentsystems and groupoid models. IStudia Logica 47 (4). 1988.The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequentsystems are given for these logics, and cutelimination results are proved. In these sequentsystems the rules for the logical operations are never changed…Read more

The Carcinogenic ExampleLogic Journal of the IGPL 5 (6): 795810. 1997.

Truth, reflection, and hierarchiesSynthese 142 (3). 2005.A common objection to hierarchical approaches to truth is that they fragment the concept of truth. This paper defends hierarchical approaches in general against the objection of fragmentation. It argues that the fragmentation required is familiar and unproblematic, via a comparison with mathematical proof. Furthermore, it offers an explanation of the source and nature of the fragmentation of truth. Fragmentation arises because the concept exhibits a kind of failure of closure under reflection. …Read more

The strengthened liar, the expressive strength of natural languages, and regimentationPhilosophical Forum 34 (34). 2003.

Giles's game and the proof theory of łukasiewicz logicStudia Logica 92 (1). 2009.In the 1970s, Robin Giles introduced a game combining Lorenzenstyle dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof…Read more

Equiparadoxicality of Yablo's Paradox and the LiarJournal of Logic, Language and Information 22 (1): 2331. 2013.It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is nonselfreferential. Rather, it giv…Read more
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PhilPapers Editorships
Revision Theory of Truth 
Proof Theory 