•  105
    Canonical Extensions and Relational Completeness of Some Substructural Logics
    with Mai Gehrke and Alessandra Palmigiano
    Journal of Symbolic Logic 70 (3). 2005.
    In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion
  •  155
    Relevance logics and relation algebras
    with Katalin Bimbó and Roger D. Maddux
    Review of Symbolic Logic 2 (1): 102-131. 2009.
    Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are sha…Read more
  •  167
    Star and perp: Two treatments of negation
    Philosophical Perspectives 7 331-357. 1993.
  •  154
    Kripke models for linear logic
    with Gerard Allwein
    Journal of Symbolic Logic 58 (2): 514-545. 1993.
    We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operat…Read more
  •  100
    Positive modal logic
    Studia Logica 55 (2). 1995.
    We give a set of postulates for the minimal normal modal logicK + without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are.
  •  70
  •  39
    E, r, and γ
    with Robert K. Meyer
    Journal of Symbolic Logic 34 (3): 460-474. 1969.
  •  178
    The substitution interpretation of the quantifiers
    with Nuel D. Belnap
    Noûs 2 (2): 177-185. 1968.