The troubles with using a logical model of IR on a large collection of documents

This is a paper of two halves. First, a description of a logical model of IR known as imaging will be presented. Unfortunately due to constraints of time and computing resource this model was not implemented in time for this round of TREC. Therefore this paper's second half describes the more conventional IR model and system used to generate the Glasgow IR result set (glair1)

Non‐Classical Knowledge

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities

The troubles with using a logical model of IR on a large collection of documents

This is a paper of two halves. First, a description of a logical model of IR known as imaging will be presented. Unfortunately due to constraints of time and computing resource this model was not implemented in time for this round of TREC. Therefore this paper’s second half describes the more conventional IR model and system used to generate the Glasgow IR result set (glair1)

Critical analysis of the Carmo-Jones system of Contrary-to-Duty obligations

We offer a technical analysis of the contrary to duty system proposed in Carmo-Jones. We offer analysis/simplification/repair of their system and compare it with our own related system

Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

Conditionals and modularity in general logics

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics