Detecting embedded horn structure in propositional logic

We show that the problem of finding a maximum renamable Horn problem within a propositional satisfiability problem is NP-hard but can be formulated as a set packing and therefore a maximum clique problem, for which numerous algorithms and heuristics have been developed

Integer programming as projection

We generalise polyhedral projection (Fourier–Motzkin elimination) to integer programming (IP) and derive from this an alternative perspective on IP that parallels the classical theory. We first observe that projection of an IP yields an IP augmented with linear congruence relations and finite-domain variables, which we term a generalised IP. The projection algorithm can be converted to a branch-and-bound algorithm for generalised IP in which the search tree has bounded depth (as opposed to conventional branching, in which there is no bound). It also leads to valid inequalities that are analogous to Chvátal–Gomory cuts but are derived from congruences rather than rounding, and whose rank is bounded by the number of variables. Finally, projection provides an alternative approach to IP duality. It yields a value function that consists of nested roundings as in the classical case, but in which ordinary rounding is replaced by rounding to the nearest multiple of an appropriate modulus, and the depth of nesting is again bounded by the number of variables. For large perturbations of the right-hand sides, the value function is shift periodic and can be interpreted economically as yielding “average” shadow prices

The Basic Communication Course Syllabus as a Rhetorical Document: The Impact of Mediated Immediacy on Communication Apprehension with Instructors and Out-of-Class Communication

The purpose of this study was to examine teachers’ use of mediated immediacy in a syllabus to determine effects on students’ communication apprehension with instructors and student out-of-class communication with instructors. Participants viewed either a basic course syllabus with high levels of mediated immediacy or low levels of mediated immediacy and then completed surveys. The results showed that syllabi high in mediated immediacy made students significantly less apprehensive to communicate with instructors and more likely to engage in out-of-class communication with them. Implications for the use of mediated immediacy in syllabus construction are discussed

Partial instantiation methods for inference in first-order logic

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a dual partial instantiation approach defined by Hooker and suggest a primal-dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results