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A Metatheory of a Mechanized Object Theory
, 1994
"... In this paper we propose a metatheory, MT which represents the computation which implements its object theory, OT, and, in particular, the computation which implements deduction in OT. To emphasize this fact we say that MT is a metatheory of a mechanized object theory. MT has some "unusual" prope ..."
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Cited by 22 (10 self)
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In this paper we propose a metatheory, MT which represents the computation which implements its object theory, OT, and, in particular, the computation which implements deduction in OT. To emphasize this fact we say that MT is a metatheory of a mechanized object theory. MT has some "unusual" properties, e.g. it explicitly represents failure in the application of inference rules, and the fact that large amounts of the code implementing OT are partial, i.e. they work only for a limited class of inputs. These properties allow us to use MT to express and prove tactics, i.e. expressions which specify how to compose possibly failing applications of inference rules, to interpret them procedurally to assert theorems in OT, to compile them into the system implementation code, and, finally, to generate MT automatically from the system code. The definition of MT is part of a larger project which aims at the implementation of selfreflective systems, i.e. systems which are able to intros...
Hierarchical MetaLogics: Intuitions, Proof Theory and Semantics
, 1991
"... The goal of this paper is to provide a possible foundation for metareasoning in the fields of artificial intelligence and computer science. We first investigate the relationship that we want to hold between metatheory and objecttheory. We then outline a methodology in which reflection rules serve ..."
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Cited by 13 (9 self)
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The goal of this paper is to provide a possible foundation for metareasoning in the fields of artificial intelligence and computer science. We first investigate the relationship that we want to hold between metatheory and objecttheory. We then outline a methodology in which reflection rules serve to deductively generate a metatheory from its object theory. Finally, we apply this methodology and define a hierarchical metalogic, namely a formal system generating an entire metahierarchy, which is sound and complete with respect to a semantics formalising the desired meta/object relationship.
Plan Formation and Execution in an Uniform Architecture of Declarative Metatheories
 Proc. Workshop on MetaProgramming in Logic
, 1990
"... We show how explicit control strategies can be represented in a declarative (classical) metatheory as first order formulae (proof plans). Proof plans can be reasoned about (by metatheoretic theorem proving) to modify the search strategy and "executed" (by suitably "interpreting" them in terms of ..."
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Cited by 11 (9 self)
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We show how explicit control strategies can be represented in a declarative (classical) metatheory as first order formulae (proof plans). Proof plans can be reasoned about (by metatheoretic theorem proving) to modify the search strategy and "executed" (by suitably "interpreting" them in terms of the deductive machinery implementation code) to prove a theorem in the object theory. The resulting architecture is uniform as it becomes possible to define a tower of metatheories, each using the same deductive machinery, each (but the lowest) being able to represent proof plans with formulae of the same shape. Plan formation at one level can be obtained by plan execution one level up. The realization of these ideas in the GETFOL system is briefly described via the implementation of a simplified version of the Boyer and Moore theorem prover. 1 Introduction The idea of using metatheories in theorem proving has been extensively studied in the past, a not exhaustive list is [DS79, Wey8...
A Multicontext Architecture for Formalizing Complex Reasoning
 International Journal of Intelligent Systems
, 1995
"... We propose multicontext systems (MC systems) as a formal framework for the specification of complex reasoning. MC systems provide the ability to structure the specification of "global" reasoning in terms of "local" reasoning subpatterns. Each subpattern is modeled as a deduction in a context, ..."
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Cited by 8 (0 self)
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We propose multicontext systems (MC systems) as a formal framework for the specification of complex reasoning. MC systems provide the ability to structure the specification of "global" reasoning in terms of "local" reasoning subpatterns. Each subpattern is modeled as a deduction in a context, formally defined as an axiomatic formal system. The global reasoning pattern is modeled as a concatenation of contextual deductions via bridge rules, i.e. inference rules that infer a fact in one context from facts asserted in other contexts. Besides the formal framework, in this paper we propose a three layer architecture designed to specify and automatize complex reasoning. At the first level we have objectlevel contexts (called scontexts) for domain specifications. Problem solving principles and, more in general, metalevel knowledge about the application domain is specified in a distinct context, called Problem Solving Context (PSC). On top of scontexts and PSC, we have a further context, called MT , where it is possible to specify strategies to control multicontext reasoning spanning through scontexts and PSC. We show how GETFOL can be used as a computer tool for the implementation of MC systems and for the automatization of multicontext deductions.
La Deduzione Automatica
"... Scopo di questo articolo e` dare una panoramica introduttiva alla deduzione automatica, mettendo in evidenza obiettivi, differenze e similitudini di alcuni fra i piu` importanti approcci al problema. ..."
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Scopo di questo articolo e` dare una panoramica introduttiva alla deduzione automatica, mettendo in evidenza obiettivi, differenze e similitudini di alcuni fra i piu` importanti approcci al problema.