Results 1  10
of
21
Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
Abstract

Cited by 1300 (17 self)
 Add to MetaCart
We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
The Logic of Games and its Applications
 Annals of Discrete Mathematics
, 1985
"... We develop a Logic in which the basic objects of concern are games, or equivalently, monotone predicate transforms. We give completeness and decision results and extend to certain kinds of manyperson games. Applications to a cake cutting algorithm and to a protocol for exchanging secrets, are given ..."
Abstract

Cited by 87 (5 self)
 Add to MetaCart
(Show Context)
We develop a Logic in which the basic objects of concern are games, or equivalently, monotone predicate transforms. We give completeness and decision results and extend to certain kinds of manyperson games. Applications to a cake cutting algorithm and to a protocol for exchanging secrets, are given. 1
Modal Logics and muCalculi: An Introduction
, 2001
"... We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mucalculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at modelchec ..."
Abstract

Cited by 59 (3 self)
 Add to MetaCart
We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mucalculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at modelchecking, and finally at the relationship of modal logics to other formalisms.
Process Logic: Expressiveness, Decidability, Completeness
, 1982
"... this paper have natural algebraic and topological interpretations: Let L be the Boolean algebra of formulas of PL modulo the PL axioms of Section 4, and let rim= {nXlXe Z}, fL=/fXlXe m } ..."
Abstract

Cited by 53 (1 self)
 Add to MetaCart
this paper have natural algebraic and topological interpretations: Let L be the Boolean algebra of formulas of PL modulo the PL axioms of Section 4, and let rim= {nXlXe Z}, fL=/fXlXe m }
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
Abstract

Cited by 41 (2 self)
 Add to MetaCart
. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
A Logical Study of Distributed Transition Systems
, 1995
"... We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The log ..."
Abstract

Cited by 36 (5 self)
 Add to MetaCart
We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The logic is studied to establish a variety of positive and negative results in terms of axiomatizability and decidability. Our positive results show that the step notion is amenable to logical treatment via standard techniques. They also help us to obtain a logical characterization of two well known models for distributed systems: labelled elementary net systems and labelled prime event structures. Our negative results show that demanding deterministic structures when dealing with a "noninterleaved " notion of transitions is, from a logical standpoint, very expressive. They also show that another well known model of distributed systems called asynchronous transition systems exhibits a surprising a...
Dynamic topological logic
 ANNALS OF PURE AND APPLIED LOGIC
, 2005
"... Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological inter ..."
Abstract

Cited by 28 (4 self)
 Add to MetaCart
Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4ish topological modality □ (interior), and two temporal modalities, ○ (next) and ∗ (henceforth), both interpreted using the continuous function f. In particular, ○ expresses f ’s action on X from one moment to the next, and ∗ expresses the asymptotic behaviour of f.
Logics of Dynamical Systems
"... We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded ..."
Abstract

Cited by 15 (15 self)
 Add to MetaCart
We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyberphysical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. Distributed hybrid systems combine distributed systems with hybrid systems, i.e., they are multiagent hybrid systems that interact through remote communication or physical interaction. Stochastic hybrid systems combine stochastic
Propositional dynamic logic of flowcharts
 Infor. and Control
, 1985
"... Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata o~¢er atomic programs and tests (i.e., flowcharts), rather than regular expressions. While the resulting version of PDL, call it APDL, is clearly equivalent in expressive p ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata o~¢er atomic programs and tests (i.e., flowcharts), rather than regular expressions. While the resulting version of PDL, call it APDL, is clearly equivalent in expressive power to PDL, it is also (in the worst case) exponentially more succinct. In particular, deciding its validity problem by reducing it to that of PDL leads to a double exponential time procedure, although PDL itself is decidable in exponential time. We present an elementary combined proof of the completeness of a simple axiom system for APDL and decidability of the validity problem in exponential time. The results are thus stronger than those for PDL, since PDL can be encoded in APDL with no additional cost, and the proofs simpler, since induction on the structure of programs is virtually eliminated. Our axiom system for APDL relates to the PDL system just as Floyd's proof method for partial correctness relates to Hoare's. © 1985 Academic Press, Inc. 1.