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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. ..."
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Cited by 1107 (16 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
A Logic for Reasoning about Probabilities
 Information and Computation
, 1990
"... We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable ( ..."
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Cited by 214 (19 self)
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We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by DempsterShafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satistiability is NPcomplete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.
Knowledge, probability, and adversaries
 Journal of the ACM
, 1993
"... Abstract: What should it mean for an agent toknowor believe an assertion is true with probability:99? Di erent papers [FH88, FZ88a, HMT88] givedi erent answers, choosing to use quite di erent probability spaces when computing the probability that an agent assigns to an event. We showthat each choice ..."
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Cited by 72 (24 self)
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Abstract: What should it mean for an agent toknowor believe an assertion is true with probability:99? Di erent papers [FH88, FZ88a, HMT88] givedi erent answers, choosing to use quite di erent probability spaces when computing the probability that an agent assigns to an event. We showthat each choice can be understood in terms of a betting game. This betting game itself can be understood in terms of three types of adversaries in uencing three di erent aspects of the game. The rst selects the outcome of all nondeterministic choices in the system� the second represents the knowledge of the agent's opponent in the betting game (this is the key place the papers mentioned above di er) � the third is needed in asynchronous systems to choose the time the bet is placed. We illustrate the need for considering all three types of adversaries with a number of examples. Given a class of adversaries, we show howto assign probability spaces to agents in a way most appropriate for that class, where \most appropriate " is made precise in terms of this betting game. We conclude by showing how di erent assignments of probability spaces (corresponding to di erent opponents) yield di erent levels of guarantees in probabilistic coordinated attack.
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 ..."
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Cited by 39 (2 self)
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. 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...
Establishing Qualitative Properties for Probabilistic Lossy Channel Systems: an Algorithmic Approach
 In Proceedings of 5th International AMAST Workshop on RealTime and Probabilistic Systems (ARTS’99
, 1999
"... . Lossy channel systems (LCSs) are models for communicating systems where the subprocesses are linked via unbounded FIFO channels which might lose messages. Link protocols, such as the Alternating Bit Protocol and HDLC can be modelled with these systems. The decidability of several verification ..."
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Cited by 23 (5 self)
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. Lossy channel systems (LCSs) are models for communicating systems where the subprocesses are linked via unbounded FIFO channels which might lose messages. Link protocols, such as the Alternating Bit Protocol and HDLC can be modelled with these systems. The decidability of several verification problems of LCSs has been investigated by Abdulla & Jonsson [AJ93,AJ94], e.g. they have shown that the reachability problem for LCSs is decidable while LTL model checking is not. In this paper, we consider probabilistic LCSs (which are LCSs where the transitions are augmented with appropriate probabilities) as introduced by [IN97] and show that the question of whether or not a linear time property holds with probability 1 is decidable. More precisely, we show how LTL nX model checking for (certain types of) probabilistic LCSs can be reduced to a reachability problem in a (nonprobabilistic) LCS where the latter can be solved with the methods of [AJ93]. 1 1 Introduction Traditiona...
Reasoning about knowledge and probability: preliminary report
 Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge
, 1988
"... Abstract: We provide a model for reasoning about knowledge anti probability together. We a.llow explicit mention of probabilities in formulas, so that our language has formulas tha.t essentia.lly say "a.ccording to agent i, formula. (p holds with probability a.t least o~. " The language i ..."
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Cited by 12 (7 self)
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Abstract: We provide a model for reasoning about knowledge anti probability together. We a.llow explicit mention of probabilities in formulas, so that our language has formulas tha.t essentia.lly say "a.ccording to agent i, formula. (p holds with probability a.t least o~. " The language is powerfid enough to allow reasoning a~bout higherorder probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, a.nd consider various properties that might hold of the interrelationship between agents ' subjective probability spaces at different states. We provide a. complete a.xiomatiza.tion for rea.soning about knowledge a.nd probability, prove a. small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a. probabilistic va.ria.nt of common knowledge to the language.
Hybrid Probabilistic Logic Programs
 Journal of Logic Programming
, 2000
"... Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theor ..."
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Cited by 10 (2 self)
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Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theory for TPLPs, and show that the fixpoint theory may be used to enumerate consequences of a TPLP in a sound and complete manner. Likewise the proof theory provides a sound and complete inference system. Last, but not least, we provide complexity results for TPLPs, showing in particular, that reasonable classes of TPLPs have polynomial data complexity. 1 Introduction There are a vast number of applications where uncertainty and time are indelibly intertwined. For example, the US Postal Service (USPS) as well as most commercial shippers have detailed statistics on how long shipments take to reach their destinations. Likewise, we are working on a Viennese historical land deed application where the precise time at which certain properties passed from one owner to another is also highly uncertain. Historical radio carbon dating methods are yet another source of uncertainty, providing approximate information about when a piece was created. Logical reasoning in situations involving temporal uncertainty is definitely important. For example, an individual querying the USPS express mail tracking system may want to know when he can expect his package to be delivered today he may then choose to stay home during the period when the probability of delivery seems very high, and leave a note authorizing the delivery official to leave the package by the door at other times.
A Logic of Probability With Decidable ModelChecking
, 2001
"... A predicate logic of probability, close to logics of probability of Halpern and al., is introduced. We consider the following modelchecking problem: for a formula and a nite state Markov chain to decide whether this formula holds on the structure dened by this Markov chain. It is shown that the mod ..."
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Cited by 6 (0 self)
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A predicate logic of probability, close to logics of probability of Halpern and al., is introduced. We consider the following modelchecking problem: for a formula and a nite state Markov chain to decide whether this formula holds on the structure dened by this Markov chain. It is shown that the modelchecking problem is decidable for a rather large subclass of formulas of a secondorder monadic logic of probability. The validity problem of the propositional fragment of this logic of probability is shown to be decidable.
unknown title
, 1999
"... Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theor ..."
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Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theory for TPLPs, and show that the fixpoint theory may be used to enumerate consequences of a TPLP in a sound and complete manner. Likewise the proof theory provides a sound and complete inference system. Last, but not least, we provide complexity results for TPLPs, showing in particular, that reasonable classes of TPLPs have polynomial data complexity. 1 Introduction There are a vast number of applications where uncertainty and time are indelibly intertwined. For example, the US Postal Service (USPS) as well as most commercial shippers have detailed statistics on how long shipments take to reach their destinations. Likewise, we are working on a Viennese historical land deed application where the precise time at which certain properties passed from one owner to another is also highly uncertain. Historical radio carbon dating methods are yet another source of uncertainty, providing approximate information about when a piece was created. Logical reasoning in situations involving temporal uncertainty is definitely important. For example, an individual querying the USPS express mail tracking system may want to know when he can expect his package to be delivered today he may then choose to stay home during the period when the probability of delivery seems very high, and leave a note authorizing the delivery official to leave the package by the door at other times.