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Multilanguage Hierarchical Logics (or: How We Can Do Without Modal Logics)
, 1994
"... MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to ..."
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Cited by 208 (51 self)
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MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to modal logics. The motivations of our proposal are technical, epistemological and implementational. From a technical point of view, we prove, among other things, that the set of theorems of the most common modal logics can be embedded (under the obvious bijective mapping between a modal and a first order language) into that of the corresponding ML systems. Moreover, we show that ML systems have properties not holding for modal logics and argue that these properties are justified by our intuitions. This claim is motivated by the study of how ML systems can be used in the representation of beliefs (more generally, propositional attitudes) and provability, two areas where modal logics have been extensively used. Finally, from an implementation point of view, we argue that ML systems resemble closely the current practice in the computer representation of propositional attitudes and metatheoretic theorem proving.
Reasoning Theories  Towards an Architecture for Open Mechanized Reasoning Systems
, 1994
"... : Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems ..."
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Cited by 47 (11 self)
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: Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and hum...
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...
The OMRS Project: State of the Art
, 1998
"... The state of the art for reasoning systems is unsatisfactory in several respects. In most cases, provers are poorly specified, hardly interconnectible, and they require a deep insight of their custom features in order to fully exploit their capabilities. The OMRS project is aimed at providing a gene ..."
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Cited by 1 (0 self)
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The state of the art for reasoning systems is unsatisfactory in several respects. In most cases, provers are poorly specified, hardly interconnectible, and they require a deep insight of their custom features in order to fully exploit their capabilities. The OMRS project is aimed at providing a general framework for specifying, structuring, and interoperating provers. This paper surveys the current achievements of the research performed within the OMRS project, under both the theoretical and the experimental side, and provides a perspective of its future evolution.
A set of hierarchically structured decision procedures for some subclasses of First Order Logic
, 1991
"... In this paper we present a complete decider for the subclass of first order logic (FOL) of the prenex universalexistential formulas not containing function symbols. The decider is composed of a set of decision procedures for simpler subclasses of FOL. By looking at the structure of the formula t ..."
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Cited by 1 (0 self)
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In this paper we present a complete decider for the subclass of first order logic (FOL) of the prenex universalexistential formulas not containing function symbols. The decider is composed of a set of decision procedures for simpler subclasses of FOL. By looking at the structure of the formula to be proved, different decision procedures (with different time complexity) are applied. Each decision procedure is built on top of one another, down to the propositional decider which is the core of the whole system. Any procedure (except the propositional one) rewrites the input formula onto a logically equivalent formula belonging to a simpler class. A claim is made that the underlying hypotheses have allowed to construct a highly structured, very efficient decider.
A Many Sorted Natural Deduction
, 1994
"... The goal of this paper is to motivate and define yet another sorted logic, called SND. All the previous sorted logics which can be found in the Artificial Intelligence literature have been designed to be used in (completely) automated deduction. SND has been designed to be used in interactive theor ..."
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The goal of this paper is to motivate and define yet another sorted logic, called SND. All the previous sorted logics which can be found in the Artificial Intelligence literature have been designed to be used in (completely) automated deduction. SND has been designed to be used in interactive theorem proving. Because of this shift of focus, SND has been designed to satisfy three innovative design requirements; that is: it is defined on top of a natural deduction calculus, and in a way to be a definitional extension of such calculus; and it is implemented on top of its implementation. In turn, because of this fact, SND has various innovative technical properties; among them: it allows us to deal with free variables, it has no notion of wellsortedness and of wellsortedness being a prerequisite of wellformedness, its implementation is such that, in the default mode, the system behaves exactly as with the original unsorted calculus. The formal system presented here was originally defin...
Open Mechanized Reasoning Systems
, 1992
"... Contents Project Summary . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . Our previous work in mechanized reasoning systems . . . . . . . Existing reasoning systems . . . . . . . . . . . . . . . Existing logical frameworks . . . . . . . . . . . . . . Open mechani ..."
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Contents Project Summary . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . Our previous work in mechanized reasoning systems . . . . . . . Existing reasoning systems . . . . . . . . . . . . . . . Existing logical frameworks . . . . . . . . . . . . . . Open mechanized reasoning systems . . . . . . . . . . . . Project Description . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accomplishments of Previous NSF Support . . . . . . . . . . Budget Pages . . . . . . . . . . . . . . . . . . . Biography of McCarthy . . . . . . . . . . . . . . . . Biography of Giunchiglia . . . . . . . . . . . . . . . Biography of Talcott . . . . . . . . . . . . . . . . i 1. Project summary There is a growing interest in the interconnection and integration of reasoning modules and systems. For example, developers of hardware veri
La Deduzione Automatica
, 1994
"... 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.
Reasoning by Analogy via Abstraction
, 1996
"... ion Adolfo Villafiorita January 1996 Technical Report MRG/DIST # 960030 universit`a di genova facolt`a di ingegneria dipartimento informatica sistemistica telematica Reasoning by Analogy via Abstraction Adolfo Villafiorita Mechanized Reasoning Group I. I., University of Ancona, via B ..."
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ion Adolfo Villafiorita January 1996 Technical Report MRG/DIST # 960030 universit`a di genova facolt`a di ingegneria dipartimento informatica sistemistica telematica Reasoning by Analogy via Abstraction Adolfo Villafiorita Mechanized Reasoning Group I. I., University of Ancona, via Brecce Bianche, 60131 Ancona, Italy, DIST, University of Genova, viale Causa 15, 16146 Genova, Italy. adolfo@mrg.dist.unige.it Abstract Abstraction has been used in theorem proving as a heuristic to reduce the search space (see, for instance, [ Simpson, 1988 ] ) and as a tool for explanation (see, for instance, [ Bundy et al., 1993 ] ). We use abstraction to model certain forms of reasoning by analogy. 1 Introduction Reasoning by analogy can be described as the process of finding the solution of a problem (the target problem) by using the known solution of a similar problem (the source problem). This process consists of "extracting" the relevant information from the source problem,...