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14
Local models semantics, or contextual reasoning = locality + compatibility
 Artificial Intelligence
, 2001
"... In this paper we present a new semantics, called Local Models Semantics, and use it to provide a foundation to reasoning with contexts. This semantics captures and makes precise the two main intuitions underlying contextual reasoning: (i) reasoning is mainly local and uses only part of what is poten ..."
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Cited by 189 (24 self)
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In this paper we present a new semantics, called Local Models Semantics, and use it to provide a foundation to reasoning with contexts. This semantics captures and makes precise the two main intuitions underlying contextual reasoning: (i) reasoning is mainly local and uses only part of what is potentially available (e.g., what is known, the available inference procedures), this part is what we call context (of reasoning); however (ii) there is compatibility among the reasoning performed in different contexts. We validate our semantics by formalizing two important forms of contextual reasoning: reasoning with viewpoints and reasoning about belief.
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 180 (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.
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&q ..."
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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...
ML systems: A Proof Theory for Contexts
, 2001
"... In the last decade the concept of context has been extensively exploited in many research areas, e.g., distributed artificial intelligence, multi agent systems, distributed databases, information integration, cognitive science, and epistemology. Three alternative approaches to the formalization of t ..."
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Cited by 12 (5 self)
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In the last decade the concept of context has been extensively exploited in many research areas, e.g., distributed artificial intelligence, multi agent systems, distributed databases, information integration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion of context have been proposed: Giunchiglia and Serafini's Multi Language Systems (ML systems), McCarthy's modal logics of contexts, and Gabbay's Labelled Deductive Systems. Previous papers have argued in favor of ML systems with respect to the other approaches. Our aim in this paper is to support these arguments from a theoretical perspective. We provide a very general definition of ML systems, which covers all the ML systems used in the literature, and we develop a proof theory for an important subclass of them: the MR systems. We prove various important results; among other things, we prove a normal form theorem, the subformula property, and the decidability of an important instance of the class of the MR systems. The paper concludes with a detailed comparison among the alternative approaches.
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 deduc ..."
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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.
A Logic of Belief and a Model Checking Algorithm for Security Protocols
, 2000
"... Model checking is a very successful technique which has been applied in the design and verification of finite state concurrent reactive processes. In this paper we show how this technique can be used for the verification of security protocols using a logic of belief. The underlying idea is to trea ..."
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Cited by 6 (2 self)
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Model checking is a very successful technique which has been applied in the design and verification of finite state concurrent reactive processes. In this paper we show how this technique can be used for the verification of security protocols using a logic of belief. The underlying idea is to treat separately the temporal evolution and the belief aspects of principals. In practice, things work as follows: when we consider the temporal evolution of a principal we treat belief atoms (namely, atomic formulae expressing belief) as atomic propositions. When we deal with the beliefs of a principal A, we model its beliefs about another principal B as the fact that A has access to a representation of B as a process. Then, any time it needs to verify the truth value of some belief atom about B, e.g., BB, A simply tests whether, e.g., holds in its (appropriate) representation of B. Beliefs are essentially used to control the "jumping" among processes. Our approach allows us to reuse the technology and tools developed in model checking.
Metaprogramming with Theory Systems
, 1995
"... A theory system is a collection of interdependent theories, some if which stand in a meta/object relationship, forming an arbitrary number of metalevels. The main thesis of this chapter is that theory systems constitute a suitable formalism for constructing advanced applications in reasoning and so ..."
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Cited by 5 (0 self)
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A theory system is a collection of interdependent theories, some if which stand in a meta/object relationship, forming an arbitrary number of metalevels. The main thesis of this chapter is that theory systems constitute a suitable formalism for constructing advanced applications in reasoning and software engineering. The Alloy language for defining theory systems is introduced, its syntax is defined and a collection of inference rules is presented. A number of problems suitable for theory systems are discussed, with program examples given in Alloy. Some current implementation issues and future extensions are discussed. This paper appears as a chapter in Metalogics and Logic Programming, edited by K. Apt and F. Turini, and published by MIT Press in 1995. 1 Outline A conventional logic program can be seen as the nonlogical axioms of a single theory. This chapter presents a thesis that we obtain a more powerful tool for applications in artificial intelligence and software engineering...
Protocols
, 2000
"... This report has been submitted for publication outside of ITC and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of ITC ..."
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This report has been submitted for publication outside of ITC and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of ITC prior to publication should be limited to peer communications and specific requests. After ouside publication, requests should be filled only by reprints or legally obtained copies of the article. A Logic of Belief and a Model Checking Algorithm for Security
Metatheories About Provability and Metatheories About Proofs in a Multicontext System
"... modify MT. MT has the good properties to do what it has been defined for. In this note, we take as a significative example the problem to reason about proof structures, possibly proofs of the same theorem. For this purpose we define a second metatheory, MP. Then, at the end the multicontext system c ..."
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modify MT. MT has the good properties to do what it has been defined for. In this note, we take as a significative example the problem to reason about proof structures, possibly proofs of the same theorem. For this purpose we define a second metatheory, MP. Then, at the end the multicontext system comprises OT, MT and MP. We claim that having two separated metatheories is natural and keeps both the metatheories significantly simpler than a single metatheory, with straightforward advantages, both for theorem proving and for representing knowledge, both intellectual and computational. The aim of this note is to define formally MP, to compare MP with MT and to show how the two different metatheories can be used to perform different kinds of metareasoning, and how they can be integrated in a multilangage system. 1 2 Two different metatheories for two different goals Here we describe the crucial features of the two metatheories. MT: the metatheory MT has b
Valid Extensions of Introspective Systems: A Foundation for Reflective Theorem Provers
, 1994
"... Introspective systems have been proved useful in several applications, especially in the area of automated reasoning. In this paper we propose to use structured algebraic specifications to describe the embedded account of introspective systems. Our main result is that extending such an introspective ..."
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Introspective systems have been proved useful in several applications, especially in the area of automated reasoning. In this paper we propose to use structured algebraic specifications to describe the embedded account of introspective systems. Our main result is that extending such an introspective system in a valid manner can be reduced to development of correct software. Since sound extension of automated reasoning systems again can be reduced to valid extension of introspective systems, our work can be seen as a foundation for extensible introspective reasoning systems, and in particular for reflective provers. We prove correctness of our mechanism and report on first experiences we have made with its realization in the KIV system (Karlsruhe Interactive Verifier).