Recent improvements in satisfiability algorithms for propositional logic have made partial instantiation methods for first order predicate logic computationally more attractive. Two such methods have been proposed, one by R. Jeroslow and a hypergraph method for datalog formulas by G. Gallo and G. Rago. We show that they are instances of two general approaches to partial instantiation, and we develop these approaches for a large decidable fragment of first order logic (the 98 fragment). 1 Introduction The last few years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods...

This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically. 1

We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral projection partially solves this problem and in particular derives precisely those inferences that can be obtained by a certain form of unit resolution. We prove that this unit resolution algorithm is exponential in the number of atoms in the restricted set but is polynomial in the problem size when this number of fixed. We also survey a number of new satisfiability algorithms that have been suggested by the polyhedral interpretation of propositional logic. 1 Introduction The inference problem in propositional logic is closely connected with polyhedral theory. In the last few years this connection has suggested a number of new inference algorithms that have substantially advanced the st...

Several logics for reasoning under uncertainty distribute "probability mass" over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear program package can implement these logics computationally if one "plugs in" a different column generation subroutine for each logic. 1 Introduction Several logics for reasoning under uncertainty are variations on a theme. Numbers, perhaps probabilities, are assigned to propositions to indicate degrees of confidence. The object is to determine the degree of confidence one can have in a conclusion inferred from the propositions. Dependencies among the propositions require that some of the "probability mass" assigned to one proposition be distributed to others. Solution of this distributio...

We describe how to combine probabilistic logic and Bayesian networks to obtain a new framework ("Bayesian logic") for dealing with uncertainty and causal relationships in an expert system. Probabilistic logic, invented by Boole, is a technique for drawing inferences from uncertain propositions for which there are no independence assumptions. A Bayesian network is a "belief net" that can represent complex conditional independence assumptions. We show how to solve inference problems in Bayesian logic by applying Benders decomposition to a nonlinear programming formulation. We also show that the number of constraints grows only linearly with the problem size for a large class of networks. INTRODUCTION Suppose we have the following database: x 1 (1) x 1 oe x 2 x 2 oe x 3 Supported in part by U. S. Air Force Office of Scientific Research, grant number AFOSR-0292 where x 1 , x 2 and x 3 are atomic propositions, and x 1 oe x 2 is the material conditional, "if x 1 , then x 2 ." Assume f...

this paper is that past failures and countermeasures are imbedded in present-day work arrangements, communication, and artifacts. These phenomena are reified versions of past labor (Latour 1994). A synchronic structural analysis must therefore be supplemented with a diachronic narrative analysis of errors and countermeasures.