Skolem Redux

Skolem fragments

W. V. Quine splits the fundamental question of ontology—What is there?—into two questions: What does a theory say that there is? and What theories ought we adopt? Of these, only the former seems amenable to philosophical treatment. Quine thus attempts to formulate an adequate criterion of ontological commitment. Syntactically, the initially existentially quantified sentences of a theory appear ...

Skolem Machines

The Skolem machine is a Turing-complete machine model where the instructions are first-order formulas of a specific form. We introduce Skolem machines and prove their logical correctness and completeness. Skolem machines compute queries for the Geolog language, a rich fragment of first-order logic. The concepts of Geolog trees and complete Geolog trees are defined, and these tree concepts are u...

Skolem arrays and skolem labellings of ladder graphs

How many neutrophils are enough (redux, redux)?

Many chemotherapeutic regimens produce neutropenia, which predisposes to microbial infection. However, not all neutropenic individuals develop infections, so the ability to predict this outcome would be a powerful clinical tool. In this issue of the JCI, Malka et al. describe a dynamic system model of neutrophil bactericidal activity that confirms and extends the concept of critical neutrophil ...

Skolem Functions for DQBF

We consider the problem of computing Skolem functions for satisfied dependency quantified Boolean formulas (DQBFs). We show how Skolem functions can be obtained from an elimination-based DQBF solver and how to take preprocessing steps into account. The size of the Skolem functions is optimized by don’t-care minimization using Craig interpolants and rewriting techniques. Experiments with our DQB...