María Manzano

Descriptive dynamic logic and its application to reflective architectures

In Artificial Intelligence, Multi-Language Logical Architectures, MLA for short, (MC [Giunchiglia and Serefini, 1994; Giunchiglia and Traverso, 1991; Giunchiglia et al., 1993], BMS [Tan, 1992], ML 2 [Balder et al., 1993], DESIRE [Treur, 1992], MILORD — II [Agusti et al., 1991; Agusti et al.,1994; Sierra and Godo, 1993], OMEGA [Attardi and Simi, 1995], FOL [Weyhrauch, 1980]) are particular types of architectures, used to build knowledge-based systems, that play a major role in dealing with complex reasoning patterns, such as those involved in non-monotonic reasoning, scheduling or planning. Despite the fact that many commonalities can be intuitively found [F. Van Harmelen et al.,1993], there was a lack of formal frameworks to compare and describe them. These architectures are based on the use of several logical languages to define local theories (or meta-theories acting upon theories) that influence/modify each other. These influences are modeled by complex control patterns of the reasoning flow between system units (also called modules or contexts) containing different knowledge theories evolving in time. Furthermore, the control patterns are often dynamically changed at run time. Therefore, when trying to define a formal framework to describe multi-language architectures it is mandatory that such a framework be able to model this dynamic behaviour.

Completeness in Hybrid Type Theory

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret

Completeness: from Gödel to Henkin

@_i

Henkin on Completeness

in propositional and first-order hybrid logic. This means: interpret

Editorial ‘Tools for Teaching Logic’

@_i\alpha _a

Diagonalisation and Church's Thesis: Kleene's Homework

, where

A note on Visions of Henkin

\alpha _a

Visions of Henkin

is an expression of any type

April the 19th

a

Henkin and Hybrid Logic

, as an expression of type