Alternative completeness theorems for modal systems.

Completeness Theorems for Syllogistic Fragments

Traditional syllogisms involve sentences of the following simple forms: All X are Y , Some X are Y , No X are Y ; similar sentences with proper names as subjects, and identities between names. These sentences come with the natural semantics using subsets of a given universe, and so it is natural to ask about complete proof systems. Logical systems are important in this area due to the prominenc...

Analyzing completeness of axiomatic functional systems for temporal × modal logics

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties of the accessibility functions (being injective, surjective, increasing, etc.) have been considered and axiomatic systems (called functional) which define t...

Completeness in modal logic

Completeness and Herbrand theorems for nominal logic

Nominal logic is a variant of first-order logic in which abstract syntax with names and binding is formalized in terms of two basic operations: name-swapping and freshness. It relies on two important principles: equivariance (validity is preserved by name-swapping), and fresh name generation (“new” or fresh names can always be chosen). It is inspired by a particular class of models for abstract...

Alternative Theorems for Nonlinear

This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of several special cases such as nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems, and then two suucient existence conditions, are established for this class of nonlinear projection eq...