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Contextual Reasoning
 EPISTEMOLOGIA, SPECIAL ISSUE ON I LINGUAGGI E LE MACCHINE
, 1992
"... It is widely agreed on that most cognitive processes are contextual in the sense that they depend on the environment, or context, inside which they are carried on. Even concentrating on the issue of contextuality in reasoning, many different notions of context can be found in the Artificial Intel ..."
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Cited by 73 (5 self)
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It is widely agreed on that most cognitive processes are contextual in the sense that they depend on the environment, or context, inside which they are carried on. Even concentrating on the issue of contextuality in reasoning, many different notions of context can be found in the Artificial Intelligence literature. Our intuition is that reasoning is usually performed on a subset of the global knowledge base. The notion of context is used as a means of formalizing this idea of localization. Roughly speaking, we take a context to be the set of facts used locally to prove a given goal plus the inference routines used to reason about them (which in general are different for different sets of facts). Our perspective is similar to that proposed in [McC87, McC91]. The goal of this paper is to propose an epistemologically adequate theory of reasoning with contexts. The emphasis is on motivations and intuitions, rather than on technicalities. The two basic definitions are reported i...
Proof Planning By Abstraction
, 1994
"... Devising powerful heuristics or shifting the control to humans have probably been the two most common solutions to keep the search space in theorem proving manageable. In this paper we take advantage of both, by using abstraction [GW92b] as a tool to plan proofs by induction and by proving its eecti ..."
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Cited by 2 (1 self)
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Devising powerful heuristics or shifting the control to humans have probably been the two most common solutions to keep the search space in theorem proving manageable. In this paper we take advantage of both, by using abstraction [GW92b] as a tool to plan proofs by induction and by proving its eectiveness in ABSFOL (an interactive theorem prover built on top of GETFOL [GT91]). 1 Introduction The complexity of problems in logic is a limit to the results that can be achieved by theorem provers; hence the need of developing powerful heuristics, or of shifting the control to humans. We have chosen both solutions, by developing and using an interactive theorem prover which implements abstraction. ABSFOL [GW92a, GSVW96, Vil93] is a theorem prover built on top of GETFOL [GT91] 1 ; ABSFOL provides tools for using abstractions and inherits from GETFOL all the tools for building proofs. Abstraction is a powerful heuristic which captures the idea of simplication of a problem: when reasoni...
A System for MultiLevel Mathematical Reasoning
, 1990
"... We present a system, called GETFOL, where, for any given mathematical object theory, it is possible to define a provably correct and complete metatheory MT. Theorem proving in MT can be used to build metatheoretic representations of object level proofs. Within GETFOL, these representations can be ..."
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Cited by 1 (1 self)
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We present a system, called GETFOL, where, for any given mathematical object theory, it is possible to define a provably correct and complete metatheory MT. Theorem proving in MT can be used to build metatheoretic representations of object level proofs. Within GETFOL, these representations can be executed to prove object level theorems. Mathematical proofs can thus be built by intermixing reasoning in the object theory and reasoning in the metatheory. This provides a very flexible way to mechanize mathematical reasoning.
Multicontext Systems as a Tool to Model Temporal Evolution
, 1993
"... Contexts are defined as axiomatic formal systems. More than one context can be defined, each one modeling/solving (part of) the problem. The (global) model/solution of the problem is obtained making contexts communicate via bridge rules. Bridge rules and contexts are the components of Multi Cont ..."
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Cited by 1 (1 self)
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Contexts are defined as axiomatic formal systems. More than one context can be defined, each one modeling/solving (part of) the problem. The (global) model/solution of the problem is obtained making contexts communicate via bridge rules. Bridge rules and contexts are the components of Multi Context systems. In this paper we want to study the applicability of multi contexts systems to reason about temporal evolution.
An Abstraction for Boolean Algebra
, 1994
"... Proof Checker. AI*IA Notizie, 2:4153, 1993. [Sim88] A. Simpson. Grazing: A Stand Alone Tactic for Theoretical Inference. Master's thesis, Dept. of Artificial Intelligence, University of Edinburgh, 1988. [SVG94] R. Sebastiani, A. Villafiorita, and F. Giunchiglia. Proving Theorems by Using Abstracti ..."
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Proof Checker. AI*IA Notizie, 2:4153, 1993. [Sim88] A. Simpson. Grazing: A Stand Alone Tactic for Theoretical Inference. Master's thesis, Dept. of Artificial Intelligence, University of Edinburgh, 1988. [SVG94] R. Sebastiani, A. Villafiorita, and F. Giunchiglia. Proving Theorems by Using Abstraction Interactively. In To appear in the proceedings of the Second International RoundTable on Abstract Intelligent Agent, Rome, Italy, 1994. Also IRSTTechnical Report 940317, IRST, Trento, Italy. [Ver93] Bob Veroff. Problem set. Association for Automated Reasoning Newsletter, (24):8, November 1993. [Vil93] A. Villafiorita. Progetto e sviluppo di un dimostratore per astrazione. Technical Report Thesis, DIST  University of Genova, 1993. [VS94] A. Villafiorita and R. Sebastiani. Proof planning by abstraction. In Proocedings of ECAI94, Workshop: From Theorem Provers to Mathematical Assistants: Issues and Possible Solutions, pages 1524, 1994. [Zha94] Hantao Zhang. Automatic proof of some bo...
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.