Cross-linguistic generalizations about grammatical contexts favoring syncretism often have an implicational form. This paper shows that this is expected if (i) morphological paradigms are required to be both as small and unambiguous possible, (ii) languages may prioritize these requirements differently, (iii) probability distributions for features interacting in syncretic patterns fixed across ...

If S is a semilattice with operators, then there is an implicational theory Q such that the congruence lattice Con(S) is isomorphic to the lattice of all implicational theories containing Q. The author and Kira Adaricheva have shown that lattices of quasi-equational theories are isomorphic to congruence lattices of semilattices with operators [1]. That is, given a quasi-equational theory Q, the...

We survey and compare parameterizations of the propositional satisfiability problem (SAT) in the framework of Parameterized Complexity (Downey and Fellows, 1999). In particular, we consider (a) parameters based on structural graph decompositions (tree-width, branch-width, and clique-width), (b) a parameter emerging from matching theory (maximum deficiency), and (c) a parameter defined by transl...

Cysouw (this volume) argues against the use of implicational universals in linguistic typology. While some of the points he makes are valid, his argumentation is in other places somewhat confused. I attempt in this paper to give some clarity to some of the issues, drawing on examples based on my typological database (Dryer 1989, 1991, 1992, 1997, 1998), which currently contains data for over 12...

Consider the problem which set V of propositional variables suffices for StabV `i A whenever `c A, where StabV := {¬¬P → P | P ∈ V }, and `c and `i denote derivability in classical and intuitionistic implicational logic, respectively. We give a direct proof that stability for the final propositional variable of the (implicational) formula A is sufficient; as a corollary one obtains Glivenko’s t...

This dissertation examines the semantic underpinnings of argument realization. Much recent work in argument realization is based on some notion of “prominence preservation,” wherein the morphosyntactic prominence of an argument in the clause (e.g. its grammatical relation) supposedly reflects its prominence in the meaning of the clause. I explore prominence preservation as it applies to crossli...

We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally we present two "concrete" dualities occuring in social choice an...

This paper shows undecidability of type-checking and typeinference problems in domain-free typed lambda-calculi with existential types: a negation and conjunction fragment, and an implicational fragment. These are proved by reducing type-checking and type-inference problems of the domain-free polymorphic typed lambda-calculus to those of the lambda-calculi with existential types by continuation...