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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 178 (47 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.
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...
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...
Introspective Metatheoretic Reasoning
 IN PROC. OF META94, WORKSHOP ON METAPROGRAMMING IN LOGIC
, 1994
"... This paper describes a reasoning system, called GETFOL, able to introspect (the code implementing) its own deductive machinery, to reason deductively about it in a declarative metatheory and to produce new executable code which can then be pushed back into the underlying implementation. In this ..."
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Cited by 15 (6 self)
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This paper describes a reasoning system, called GETFOL, able to introspect (the code implementing) its own deductive machinery, to reason deductively about it in a declarative metatheory and to produce new executable code which can then be pushed back into the underlying implementation. In this paper we discuss the general architecture of GETFOL and the problems related to its implementation.
Hierarchical MetaLogics for Belief and Provability: How We Can Do Without Modal Logics
, 1992
"... 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 metatheories, each with a first order language containing names for the language below, and propose them as an a ..."
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Cited by 3 (3 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 metatheories, each with a first order language containing names for the language below, and propose them as an alternative to modal logics. The motivations of our proposal are technical and epistemological. From a technical point of view, we prove, among other things, that modal logics can be embedded in 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. We motivate our claim by studying how they can be used in the representation of beliefs (more generally, propositional attitudes) and provability, two areas where modal logics have been extensively used. 1
Computational Reflection Via Mechanized Logical Deduction
, 1993
"... REX School/Workshop on Foundations of Object Oriented Languages, Lecture Notes in Computer Science, May 1990. [Yon91] A. Yonezawa. A Reflective Object Oriented Concurrent Language. Lecture Notes in Computer Science, 441:254256, 1991. 17 [Giu92] F. Giunchiglia. The GETFOL Manual  GETFOL version ..."
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Cited by 3 (0 self)
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REX School/Workshop on Foundations of Object Oriented Languages, Lecture Notes in Computer Science, May 1990. [Yon91] A. Yonezawa. A Reflective Object Oriented Concurrent Language. Lecture Notes in Computer Science, 441:254256, 1991. 17 [Giu92] F. Giunchiglia. The GETFOL Manual  GETFOL version 1. Technical Report 920401, DIST  University of Genova, Genoa, Italy, 1992. Forthcoming IRSTTechnical Report. [GMMW77] M.J. Gordon, R. Milner, L. Morris, and C. Wadsworth. A Metalanguage for Interactive Proof in LCF. CSR report series CSR1677, Department of Artificial Intelligence, Dept. of Computer Science, University of Edinburgh, 1977. [GMW79] M.J. Gordon, A.J. Milner, and C.P. Wadsworth. Edinburgh LCF  A mechanized logic of computation, volume 78 of Lecture Notes in Computer Science. Springer Verlag, 1979. [GT91] F. Giunchiglia and P. Traverso. Reflective reasoning with and between a declarative metatheory and the implementation code. In Proc. of the 12th International Joint C
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.
Abstract Contextual Reasoning
"... 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 Intellig ..."
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Cited by 1 (0 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, see for instance [Giunchiglia 1991a,
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
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...