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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.
Multiagent Reasoning with Belief Contexts II: Elaboration Tolerance
 Intelligent Agents: Proceedings of 1994 Workshop on Agent Theories, Architectures, and Languages, number 890 in Lecture Notes in Computer Science
, 1994
"... As discussed in previous papers, belief contexts are a powerful and appropriate formalism for the representation and implementation of propositional attitudes in a multiagent environment. In this paper we show that a formalization using belief contexts is also elaboration tolerant. That is, it is a ..."
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Cited by 51 (6 self)
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As discussed in previous papers, belief contexts are a powerful and appropriate formalism for the representation and implementation of propositional attitudes in a multiagent environment. In this paper we show that a formalization using belief contexts is also elaboration tolerant. That is, it is able to cope with minor changes to input problems without major revisions. Elaboration tolerance is a vital property for building situated agents: it allows for adapting and reusing a previous problem representation in different (but related) situations, rather than building a new representation from scratch. We substantiate our claims by discussing a number of variations to a paradigmatic case study, the Three Wise Men problem. Introduction Belief contexts (Giunchiglia 1993; Giunchiglia & Serafini 1994; Giunchiglia et al. 1993) are a formalism for the representation of propositional attitudes. Their basic feature is modularity: knowledge can be distributed into different and separated mod...
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 might be ..."
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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...
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...
Program Tactics and Logic Tactics
 IN PROCEEDINGS 5TH INTNL. CONFERENCE ON LOGIC PROGRAMMING AND AUTOMATED REASONING (LPAR'94
, 1994
"... In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theor ..."
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Cited by 19 (10 self)
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In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theorem prover (we call these tactics, Program Tactics). MT is expressive enough to represent the most interesting tacticals, i.e. then, orelse, try, progress and repeat. repeat allows us to express Logic Tactics which correspond to Program Tactics which may not terminate. This work is part of a larger project which aims at the development and mechanization of a metatheory which can be used to reason about, extend and, possibly, modify the code implementing Program Tactics and the GETFOL basic inference rules.
Multicontext Systems as a Specification Framework for Complex . . .
 Formal Specification of Complex Reasoning Systems, Ellis Horwood
, 1992
"... this paper we propose multi context systems (MC systems from now on) as a logical framework for the formal specification of complex reasoning. MC systems have been motivated and formally introduced in [6, 7]; they are also called multilanguage systems (ML systems) to emphasize the fact that they all ..."
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Cited by 18 (2 self)
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this paper we propose multi context systems (MC systems from now on) as a logical framework for the formal specification of complex reasoning. MC systems have been motivated and formally introduced in [6, 7]; they are also called multilanguage systems (ML systems) to emphasize the fact that they allow the definition of multiple languages, each language associated with a context. The general idea is to model local reasoning as deduction inside a context. A context is formally defined as an axiomatic formal system, i.e. a triple consisting of a language, a set of axioms and a set of inference rules. Interaction between contexts is formalized via bridge rules, i.e. rules whose premises and conclusion belong to different contexts. The notion of deduction in an MC system (modeling the reasoning of the whole system) is defined as the composition, via bridge rules, of the contextual deductions
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.
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.
Bidirectional Natural Deduction
 AI*IA Notizie
, 1993
"... The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This pap ..."
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Cited by 4 (2 self)
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The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides basic concepts to be incorporated into an innovative theorem prover to support interactive proofs construction in general domains. 1