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Compositional Model Checking
, 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
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Cited by 2407 (62 self)
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We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.
A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 52 (3 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
A Formalization of Viewpoints
 FUNDAMENTA INFORMATICAE
, 1995
"... We present a formalisation for the notion of viewpoint , a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus through an axiomatization of provability and with the addition of proper reflection rul ..."
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Cited by 34 (3 self)
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We present a formalisation for the notion of viewpoint , a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus through an axiomatization of provability and with the addition of proper reflection rules. The extension is not conservative, but consistency is granted. Viewpoints are defined as set of reified metalevel sentences. A proof theory for viewponts is developed which enables to carry out proofs of sentences involving several viewpoints. A semantic account of viewpoints is provided, dealing with issues of self referential theories and paradoxes, and exploiting the notion of contextual entailment . Notions such as beliefs, knowledge, truth and situations can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints.
Shifting sands: An interestrelative theory of vagueness
 Philosophical Topics
, 2000
"... Please quote or cite page numbers from published version only. Saul Kripke pointed out that whether or not an utterance gives rise to a liarlike paradox cannot always be determined by checking just its form or content. 1 Whether or not Jones’s utterance of ‘Everything Nixon said is true ’ is parado ..."
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Cited by 31 (0 self)
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Please quote or cite page numbers from published version only. Saul Kripke pointed out that whether or not an utterance gives rise to a liarlike paradox cannot always be determined by checking just its form or content. 1 Whether or not Jones’s utterance of ‘Everything Nixon said is true ’ is paradoxical depends in part on what Nixon said. Something similar may be said about the sorites paradox. For example, whether or not the predicate ‘are
A revengeimmune solution to the semantic paradoxes
 Journal of Philosophical Logic
"... The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(〈A〉) ↔ A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ord ..."
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Cited by 24 (6 self)
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The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(〈A〉) ↔ A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(〈A〉) with A within the language. The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness ” predicates within the language; contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various ”levels of defectiveness ” can all be made coherent together within a single object language. 1
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...
Reasoning about conditions and exceptions to laws in regulatory conformance checking
 IN SUBMISSION: HTTP://WWW.CIS.UPENN.EDU/˜NIKHILD/REASONING.PDF (2008
, 2008
"... This paper considers the problem of checking whether an organization conforms to a body of regulation. Conformance is cast as a trace checking trace or run representing the operations of an organization. We focus on the problem of designing a logic to represent regulation. A common phenomenon in r ..."
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Cited by 14 (5 self)
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This paper considers the problem of checking whether an organization conforms to a body of regulation. Conformance is cast as a trace checking trace or run representing the operations of an organization. We focus on the problem of designing a logic to represent regulation. A common phenomenon in regulatory texts is for sentences to refer to others for conditions or exceptions. We motivate the need for a formal representation of regulation to accomodate such references between statements. We then extend linear temporal logic to allow statements to refer to others. The semantics of the resulting logic is defined via a combination of techniques from Reiter’s default logic and Kripke’s theory of truth.