Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems

Our long-term goal is the development of a general framework for specifying, structuring, and interoperating provers. Our main focus is on the formalization of the architectural and implementational choices that underlie the construction of such systems. This paper has two main goals. The first is to introduce the main intuitions underlying the proposed framework. We concentrate on its use in the integration of provers. The second is the development of the notion of reasoning theory, meant as the formalization of the notion of `implementation of the logic` of a prover. As an example we sketch an analysis, at the reasoning theory level, of the integration of linear arithmetic into the NQTHM simplification proces

Computational Reflection via Mechanized Logical Deduction

In this paper, we show how a system for automated deduction can be given computational reflection, i.e. can affect its own computation mechanism, by using the very same machinery implementing logical deduction. This feature, that we call computational reflection via mechanized logical deduction, provides both theoretical and practical advantages. First, the theorem prover can inspect, extend and modify its own underlying theorem proving strategies automatically. Second, mechanized logical deduction can be used to reason about the ways these strategies can be extended and modified and to prove correctness statements. This opens up the possibility of building systems that are able to perform correct and safe reflective self-extension and self-modification. 1 Introduction and motivations Reflective and metatheoretic reasoning are well known techniques applied in automated deduction (see for instance [23], [5], [3], [7, 17], [1]).Proof checkers and theorem provers have been proposed that ..

Towards Provably Correct System Synthesis and Extension

This paper describes the approach, what we have done so far and how we intend to proceed to pursue our ultimate goal

A Logic Level Specification of the NQTHM Simplification Process

Our ultimate goal is to provide a framework and a methodology which will allow users to construct and extend complex reasoning systems by composing existing modules in a "plug and play" manner. To this end in a previous paper we have defined a general architecture for a class of reasoning modules and systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a logic component which consists of the assertions manipulated by the OMRS and the elementary deductions upon them; a control component which consists of the inference strategies of the OMRS; an interaction component which provides the OMRS with the capability of interacting with other systems, including OMRSs and human users. We have already developed a theoretical framework underlying the logic component of this architecture. In this paper we show how this formalism can be used in practice to specify the logic component of the simplification process of NQTHM, the Boyer-Moore theorem prover. 1

Heliox administration in anesthetized rabbits with spontaneous inspiratory flow limitation

We investigated the effects of heliox administration (80% Helium in O2) on tidal inspiratory flow limitation (tIFL) occurring in supine anesthetized spontaneously breathing rabbits, regarded as an animal model of obstructive apnea-hypopnea syndrome. 22 rabbits were instrumented to record oro-nasal mask flow, airway opening, tracheal and esophageal pressures and diaphragm and genioglossus electromyographic activities while breathing either room air or heliox, and, in 12 rabbits, also during the application of continuous positive airway pressure (CPAP; 6 cmH2O). For the group, heliox increased peak inspiratory flow, ventilation (18±11%), peak inspiratory tracheal and dynamic transpulmonary pressures, but in no animal eliminated tIFL, as instead CPAP did in all. Muscle activities were unaffected by heliox. In the presence of IFL the increase in flow with heliox (DeltaVIFL) varied markedly among rabbits (2 to 49%), allowing the distinction between responders and non-responders. None of the baseline variables discriminated responders and non-responders. However, fitting the Rohrer equation (R=K1+K2V) to the tracheal pressure-flow relationship over the first 0.1s of inspiration while breathing air allowed such discrimination on the basis of larger K2 in responders (0.005±.002 vs 0.002±.001 cmH2O·s2·ml-2; p<0.001), suggesting a corresponding difference in the relative contribution of laminar and turbulent flow. The differences in DeltaVIFL between responders and non-responders were simulated by modeling the collapsible segment of the upper airways as a non-linear resistor and varying its pressure-volume curve, length and diameter, thus showing the importance of mechanical and geometrical factors in determining the response to heliox in the presence of tIFL