A Useful Four-Valued Logic

Belnap, Nuel D.

doi:10.1007/978-94-010-1161-7_2

Cited by 878 publications

(381 citation statements)

References 7 publications

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“…Instead, multi-valued structures have been employed for this task [10]. In our approach, we use the 4-valued logic known as Belnap [3] (see Fig. 3).…”

Section: Logics For Open Systemsmentioning

confidence: 99%

Finding Environment Guarantees

Chećhik

Gheorghiu

Gurfinkel

Fundamental Approaches to Software Engineering

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Abstract. When model checking a software component, a model of the environment in which that component is supposed to run is constructed. One of the major threats to the validity of this kind of analysis is the correctness of the environment model. In this paper, we identify and formalize a problem related to environment models -environment guarantees. It captures those cases where the correctness of the component under analysis is due solely to the model of its environment. Environment guarantees provides a model-based analog to a property-based notion of vacuity by identifying cases when the component is irrelevant to satisfaction of a property. The paper also presents a model checking technique for the detection of environment guarantees. We show the effectiveness of our technique by applying it to a previously published study of TCAS II, where it finds a number of environment guarantees.

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“…Instead, multi-valued structures have been employed for this task [10]. In our approach, we use the 4-valued logic known as Belnap [3] (see Fig. 3).…”

Section: Logics For Open Systemsmentioning

confidence: 99%

Finding Environment Guarantees

Chećhik

Gheorghiu

Gurfinkel

Fundamental Approaches to Software Engineering

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“…The squares that are obtained by the two-valued and the three-valued chains are shown in Figure 1. In the literature, these structures are commonly referred to as F OUR (after Belnap's [7,8] original four-valued logic) and N IN E (see e.g. [1,2]), respectively.…”

Section: Squaresmentioning

confidence: 99%

“…For this reason, several researchers have considered more elaborate means of eliciting and representing preferences. In particular, Belnap's logic F OUR [7,8], and some of its extensions, built around the truth values 'true', 'false', 'unknown' and 'contradiction', had immediate and intuitive appeal, and were taken as the basis for the approaches in [21,24,[27][28][29]. However, we found that many of these approaches lack a proper way of representing the preferences, and as a consequence no solid analysis tools nor clear strategies for decision making under incomplete and/or conflicting information are available to the reasoner in such cases.…”

Section: Introductionmentioning

confidence: 99%

Preference Modeling by Rectangular Bilattices

Arieli

Cornelis

Deschrijver

2006

Modeling Decisions for Artificial Intelligence

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Abstract. Many realistic decision aid problems are fraught with facets of ambiguity, uncertainty and conflict, which hamper the effectiveness of conventional and fuzzy preference modeling approaches, and command the use of more expressive representations. In the past, some authors have already identified Ginsberg's/Fitting's theory of bilattices as a naturally attractive candidate framework for representing uncertain and potentially conflicting preferences, yet none of the existing approaches addresses the real expressive power of bilattices, which lies hidden in their associated truth and knowledge orders. As a consequence, these approaches have to incorporate additional conventions and 'tricks' into their modus operandi, making the results unintuitive and/or tedious. By contrast, the aim of this paper is to demonstrate the potential of (rectangular) bilattices in encoding not just the problem statement, but also its generic solution strategy.

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“…We extend the notion of quantification for multi-valued reasoning by using conjunction and disjunction for universal and existential quantification, respectively. This treatment of quantification is standard [1,18]. The semantics of the operator is…”

Section: Multi-valued Ctlmentioning

confidence: 99%

“…For example, Łukasiewicz [16] first introduced a three-valued logic to allow for propositions whose truth values are 'unknown', while Belnap [1] proposed a four-valued logic that also introduces the value 'both' (i.e. "true and false"), to handle inconsistent assertions in database systems.…”

Section: Introductionmentioning

confidence: 99%

Implementing a Multi-valued Symbolic Model Checker

Chećhik

Devereux

Easterbrook

2001

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Multi-valued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. In this paper, we present an implementation of a symbolic model checker for multi-valued temporal logics. The model checker works for any multi-valued logic whose truth values form a quasiboolean lattice. Our models are generalized Kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multi-valued logic. Properties to be model checked are expressed in CTL, generalized with a multi-valued semantics. The design of the model checker is based on the use of MDDs, a multi-valued extension of Binary Decision Diagrams. We describe MDDs and their use in the model checker. We also give its theoretical time complexity and some preliminary empirical performance data.

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A Useful Four-Valued Logic

Cited by 878 publications

References 7 publications

Finding Environment Guarantees

Finding Environment Guarantees

Preference Modeling by Rectangular Bilattices

Implementing a Multi-valued Symbolic Model Checker

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