Abstract

In this paper, we focus on investigation of the predicate transformer semantics of the contract language introduced by Back and von Wright in their book titled as “Refinement Calculus: A Systematic Introduction” (Springer-Verlag, New York, 1998) in the framework of fuzziness. In order to define fuzzy operations, i.e., fuzzy logic connectives, we take into account implicator → and its associated based on residuated lattice theory. Based on these basic fuzzy operations, we introduce the angelic and demonic updates of fuzzy relations. They are the basis of fuzzy predicate transformers in the sense of that any strongly monotone fuzzy predicate transformer can be represented as the sequential composition of the angelic and demonic updates. Together with the standard strong negation , we set up the duality between the angel and demon. The fuzzy predicate transformers semantics of contract statements is established and a simple example of contract statements is given.

Highlights

  • There are four main approaches to describe the semantics of some language, i.e., the denotational [1], the operational [2], the axiomatic [3] and the algebraic [4] approaches

  • This paper focuses on the establishment of fuzzy semantics of contract language based on fuzzy predicate transformers [11]

  • We introduce the notion of strongly monotone fuzzy predicate transformers, and prove the Normal Form Theorem which shows that strongly monotone fuzzy predicate transformers can be represented as the sequential composition of the angelic and demonic updates

Read more

Summary

Introduction

There are four main approaches to describe the semantics of some language, i.e., the denotational [1], the operational [2], the axiomatic [3] and the algebraic [4] approaches. Ying sets up the probabilistic semantics of the contract statements based on the probabilistic logic through probabilistic predicate transformers [6] [9]. This paper focuses on the establishment of fuzzy semantics of contract language based on fuzzy predicate transformers [11]. Our goal is twofold: (1) We set up the fuzzy predicate transformer semantics of contract statement S, which maps a postcondition α over final states, i.e., a fuzzy predicate, into a precondition S (α ) , a fuzzy predicate over initial states. The followed is the section of conclusion and future work

Contract Language
Residuated Lattice Theory
Fuzzy Predicates
Fuzzy Predicates Transformers
Basic Predicate Transformers
Analysis
Fuzzy Semantics of Contract Language
The Duality
Monotonicity
Conclusion and Further Work
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call