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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 888 (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
A Propositional Modal Logic of Time Intervals
 Journal of the ACM
, 1996
"... : In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a gener ..."
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Cited by 128 (2 self)
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: In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a generalization of pointbased modal temporal logic. We discuss related logics, give an intuitive presentation of the new logic, and define its formal syntax and semantics. We make no assumption about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals) or not (such as the rationals). We show, however, that there are formulas in the logic that allow us to distinguish all these situations. We also give a translation of our logic into firstorder logic, which allows us to apply some results on firstorder logic to our modal one. Finally, we consider the difficulty o...
Concurrency and Communication in Transaction Logic
 IN JOINT INTL. CONFERENCE AND SYMPOSIUM ON LOGIC PROGRAMMING
, 1996
"... In previous work, we developed Transaction Logic (or T R), which deals with state changes in deductive databases. T R provides a logical framework in which elementary database updates and queries can be combined into complex database transactions. T R accounts not only for the updates themselves, bu ..."
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Cited by 63 (15 self)
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In previous work, we developed Transaction Logic (or T R), which deals with state changes in deductive databases. T R provides a logical framework in which elementary database updates and queries can be combined into complex database transactions. T R accounts not only for the updates themselves, but also for important related problems, such as the order of update operations, nondeterminism, and transaction failure and rollback. In the present paper, we propose Concurrent Transaction Logic (or CT R), which extends Transaction Logic with connectives for modeling the concurrent execution of complex processes. Concurrent processes in CT R execute in an interleaved fashion and can communicate and synchronize themselves. Like classical logic, CT R has a "Horn" fragment that has both a procedural and a declarative semantics, in which users can program and execute database transactions. CT R is thus a deductive database language that integrates concurrency, communication, and updates. All th...
A Logic For Programming Database Transactions
, 1998
"... : We propose an extension of classical predicate calculus, called Transaction Logic, which provides a logical foundation for the phenomenon of state changes in logic programs and databases. Transaction Logic comes with a natural model theory and a sound and complete proof theory. The proof theory n ..."
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Cited by 44 (22 self)
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: We propose an extension of classical predicate calculus, called Transaction Logic, which provides a logical foundation for the phenomenon of state changes in logic programs and databases. Transaction Logic comes with a natural model theory and a sound and complete proof theory. The proof theory not only verifies programs, but also executes them, which makes this logic an ideal tool for declarative programming of database transactions and statemodifying logic programs. The semantics of Transaction Logic leads naturally to features whose amalgamation in a single logic has proved elusive in the past. These features include hypothetical and committed updates, dynamic constraints on transaction execution, nondeterminism, and bulk updates. Finally, Transaction Logic holds promise as a logical model of hitherto nonlogical phenomena, including socalled procedural knowledge in AI, and the behavior of objectoriented databases, especially methods with side effects. This paper presents the...
Dynamic Linear Time Temporal Logic
 IN ANNALS OF PURE AND APPLIED LOGIC
, 1997
"... A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S ..."
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Cited by 44 (3 self)
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A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic secondorder theory of !sequences. In fact a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already as expressive as S1S. We pin down in an obvious manner the sublogic of DLTL which correponds to the first order fragment of S1S. We show that DLTL has an exponential time decision procedure. We also obtain an axiomatization of DLTL. Finally, we point to some natural extensions of the approach presented here for bringing together propositional dynamic and temporal logics in a linear time setting.
Database programming in Transaction Logic
 In Proc. 4th Int. Workshop on Database Programming Languages
, 1993
"... This paper presents database applications of the recently proposed Transaction Logic—an extension of classical predicate logic that accounts in a clean and declarative fashion for the phenomenon of state changes in logic programs and databases. It has a natural model theory and a sound and complete ..."
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Cited by 26 (13 self)
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This paper presents database applications of the recently proposed Transaction Logic—an extension of classical predicate logic that accounts in a clean and declarative fashion for the phenomenon of state changes in logic programs and databases. It has a natural model theory and a sound and complete proof theory, but, unlike many other logics, it allows users to program transactions. In addition, the semantics leads naturally to features whose amalgamation in a single logic has proved elusive in the past. Finally, Transaction Logic holds promise as a logical model of hitherto nonlogical phenomena, including socalled procedural knowledge in AI, and the behavior of objectoriented databases, especially methods with side effects. This paper focuses on the applications of T R to database systems, including transaction definition and execution, nested transactions, view updates, consistency maintenance, bulk updates, nondeterminism, sampling, active databases, dynamic integrityconstraints, hypothetical reasoning, and imperativestyle programming.
Reasoning about Action and Change  A Dynamic Logic Approach
 Journal of Logic, Language, and Information
, 1996
"... this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)the modal logic of actions and of computer programs (see Pratt, 1976, 19 ..."
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Cited by 25 (0 self)
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this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)the modal logic of actions and of computer programs (see Pratt, 1976, 1980; Segerberg 1980; Harel, 1984). It is based on the idea of associating an operator [ff] with each action ff, the brackets being reminiscient of the box operator 2 of ordinary modal logic (see Hughes & Cresswell, 1984). The reading of a formula [ff]A is "after every terminating (halting) execution of ff, A is true." PDL provides a powerful language for describing compound actions such as sequential composition of actions ff and fi, written ff; fi, (nondeterministic) choice between ff and fi, written ff + fi, and (nondeterministic) iteration of ff, written ff
Completeness of Kozen's Axiomatisation of the Propositional µCalculus
 Inform. and Comput
, 1995
"... Propositional calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this ..."
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Cited by 24 (0 self)
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Propositional calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this axiomatisation is complete.
Deductive and Object Data Languages: A Quest for Integration
 Proceedings of the International Conference on Deductive and ObjectOriented Databases
, 1995
"... . According to rumors, the early hybrids of objectoriented and deductive languages were mutants that escaped from secret Government AI labs. Whether this is true or not, the fact is that by mid80's, database and logic programming communities began to take notice. The temptation was hard to re ..."
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Cited by 21 (0 self)
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. According to rumors, the early hybrids of objectoriented and deductive languages were mutants that escaped from secret Government AI labs. Whether this is true or not, the fact is that by mid80's, database and logic programming communities began to take notice. The temptation was hard to resist: the objectoriented paradigm provides a better way of manipulating structured objects, while logic and deduction offer the power and flexibility of ad hoc querying and reasoning. Thus, hybrid languages have the potential for becoming an ideal turf for cultivating the next generation of information systems. The approaches to integration of the two paradigms range from logicbased languages with unified declarative semantics, to messagepassing prologs, to Prolog/C++ cocktails. In the past eight years, my colleagues and I have been developing a unified objectbased logic intended to capture most of the essentials of the objectoriented paradigm. The overall plot here is that once the fundament...
The power of the future perfect in program logics
 Information and Control
, 1985
"... The expressiveness of branching time tense (temporal) logics whose eventually operators are relativised to general paths into the future is investigated. These logics are interpreted in models obtained by generalising the usual notion of transition system to allow infinite transitions. It is shown t ..."
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Cited by 19 (0 self)
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The expressiveness of branching time tense (temporal) logics whose eventually operators are relativised to general paths into the future is investigated. These logics are interpreted in models obtained by generalising the usual notion of transition system to allow infinite transitions. It is shown that the presence of formulae expressing the future perfect enables one to prove that the expressiveness of the logic can be charaeterised by a notion of bisimulation on the generalised transition systems. The future perfect is obtained by adding a past tense operator to the language. Finally the power of various tense languages from the literature are