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41
Dynamic Logic
 Handbook of Philosophical Logic
, 1984
"... ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possibl ..."
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Cited by 1008 (7 self)
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ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possible values a 2 N. This operation becomes explicit in DL in the form of the program x := ?, called a nondeterministic or wildcard assignment. This is a rather unconventional program, since it is not effective; however, it is quite useful as a descriptive tool. A more conventional way to obtain a square root of y, if it exists, would be the program x := 0 ; while x < y do x := x + 1: (1) In DL, such programs are firstclass objects on a par with formulas, complete with a collection of operators for forming compound programs inductively from a basis of primitive programs. To discuss the effect of the execution of a program on the truth of a formula ', DL uses a modal construct <>', which
Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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Cited by 62 (18 self)
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
Structured Specifications and Interactive Proofs with KIV
, 1998
"... The aim of this chapter is to describe the integrated specification and theorem proving environment of KIV. KIV is an advanced tool for developing high assurance systems. It supports:  hierarchical formal specification of software and system designs  specification of safety/security models  ..."
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Cited by 36 (28 self)
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The aim of this chapter is to describe the integrated specification and theorem proving environment of KIV. KIV is an advanced tool for developing high assurance systems. It supports:  hierarchical formal specification of software and system designs  specification of safety/security models  proving properties of specifications  modular implementation of specification components  modular verification of implementations  incremental verification and error correction  reuse of specifications, proofs, and verified components KIV supports the entire design process from formal specifications to verified code. It supports functional as well as statebased modeling. KIV is ready for use, and has been tested in a number of indu...
Defaults and Revision in Structured Theories
 In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'91
, 1991
"... Starting from a logic which specifies how to make deductions from a set of sentences (a `flat theory'), a way to generalise this to a partially ordered bag of sentences (a `structured theory') is given. The partial order is used to resolve conflicts. If OE occurs below / then / is accepted ..."
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Cited by 35 (16 self)
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Starting from a logic which specifies how to make deductions from a set of sentences (a `flat theory'), a way to generalise this to a partially ordered bag of sentences (a `structured theory') is given. The partial order is used to resolve conflicts. If OE occurs below / then / is accepted only insofar as it does not conflict with OE. We start with a language L, a set of interpretations M and a satisfaction relation fl ` M \Theta L. The key idea is to define, for each structured theory, a preorder on interpretations. Models of the structured theory are defined to be maximal interpretations in the ordering. They are shown to exist if the logic hL; M; fli is compact. A revision operator is defined, which takes a structured theory and a sentence and returns a structured theory. The consequence relation has the properties of weak monotonicity, weak cut and weak reflexivity with respect to this operator, but fails their strong counterparts. 1 Introduction Ordering sentences in a theo...
Reasoning about abstract state machines: The WAM case study
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 1997
"... This paper describes the rst half of the formal verification of a Prolog compiler with the KIV ("Karlsruhe Interactive Verifier") system. Our work is based on [BR95], where an operational Prolog semantics is de ned using the formalism of Gurevich Abstract State Machines, and then refined i ..."
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This paper describes the rst half of the formal verification of a Prolog compiler with the KIV ("Karlsruhe Interactive Verifier") system. Our work is based on [BR95], where an operational Prolog semantics is de ned using the formalism of Gurevich Abstract State Machines, and then refined in several steps to the Warren Abstract Machine (WAM). We define a general translation of sequential Abstract State Machines to Dynamic Logic, which formalizes correctness of such refinement steps as a deduction problem. A proof technique for verification is presented, which corresponds to the informal use of proof maps. 6 of the 12 given refinement steps were verified. We found that the proof sketches given in [BR95] hide a lot of implicit assumptions. We report on our experiences in uncovering these assumptions incrementally during formal verification, and the support KIV offers for such `evolutionary' correctness proofs.
VSE: Formal Methods Meet Industrial Needs
, 2000
"... The Verification Support Environment (VSE) is a tool to formally specify and verify complex systems. It provides means to structure specifications and supports the development process from the specification of a system to the automatic generation of code. Formal developments following the VSE method ..."
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Cited by 11 (7 self)
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The Verification Support Environment (VSE) is a tool to formally specify and verify complex systems. It provides means to structure specifications and supports the development process from the specification of a system to the automatic generation of code. Formal developments following the VSE method are stored and maintained in an administration system that guides the user and maintains a consistent state of the development. An integrated deduction system provides proof support for the deduction problems arising during the development process. We describe the application of VSE to an industrial case study and give an overview of the enhanced VSE system and the VSE methodology.
KIV 3.0 for Provably Correct Systems
 IN CURRENT TRENDS IN APPLIED FORMAL METHODS. SPRINGER LNCS 1641
, 1999
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VSE: Controlling the Complexity in Formal Software Developments
 In Proceedings of the International Workshop on Applied Formal Methods
, 1998
"... . We give an overview of the enhanced VSE system which is a tool to formally specify and verify systems. It provides means for structuring specifications and it supports the development process from the specification of a system to the code generation. Formal developments following this method a ..."
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Cited by 8 (3 self)
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. We give an overview of the enhanced VSE system which is a tool to formally specify and verify systems. It provides means for structuring specifications and it supports the development process from the specification of a system to the code generation. Formal developments following this method are stored and maintained in an administration system that guides the user and maintains a consistent state. An integrated deduction system provides proof support for the deduction problems arising during the development process. 1 Introduction The reliability of complex software systems is becoming increasingly important for technical systems. Malfunctioning of software systems caused by design flaws or faulty implementations may lead to loss or garbling of data, breach of security, danger to life and limb, and, in almost all cases severe economic losses. In order to allow for an industrial development of software according to the highest IT security criteria (ITSEC), the VSE tool [5] ...
Temporal Logic of Programs: A Standard Approach
, 1993
"... This chapter discusses propositional and rstorder temporal logic of programs with time corresponding to integers. The logic contains past and future temporal operators. We concentrate mainly on the formal verification of temporal properties. A variety of proof systems is presented in both Hilbert a ..."
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Cited by 7 (0 self)
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This chapter discusses propositional and rstorder temporal logic of programs with time corresponding to integers. The logic contains past and future temporal operators. We concentrate mainly on the formal verification of temporal properties. A variety of proof systems is presented in both Hilbert and Gentzen styles. Various notions of soundness and completeness are investigated. We also discuss applications of the logic in the formal speci cation and verification of properties of algorithms and data structures.