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18
Expressive Logics for Coalgebras via Terminal Sequence Induction
 Notre Dame J. Formal Logic
, 2002
"... This paper introduces the proof principle of terminal sequence induction and shows, how terminal sequence induction can be used to obtain expressiveness results for logics, interpreted over coalgebras. ..."
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Cited by 26 (8 self)
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This paper introduces the proof principle of terminal sequence induction and shows, how terminal sequence induction can be used to obtain expressiveness results for logics, interpreted over coalgebras.
Halforder Modal Logic: How To Prove Realtime Properties
 IN PROCEEDINGS OF THE NINTH ANNUAL SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 1990
"... We introduce a novel extension of propositional modal logic that is interpreted over Kripke structures in which a value is associated with every possible world. These values are, however, not treated as full firstorder objects; they can be accessed only by a very restricted form of quantificati ..."
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Cited by 26 (6 self)
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We introduce a novel extension of propositional modal logic that is interpreted over Kripke structures in which a value is associated with every possible world. These values are, however, not treated as full firstorder objects; they can be accessed only by a very restricted form of quantification: the "freeze" quantifier binds a variable to the value of the current world. We present a complete proof system for this ("halforder") modal logic. As a special case, we obtain the realtime temporal logic TPTL of [AH89]: the models are restricted to infinite sequences of states, whose values are monotonically increasing natural numbers. The ordering relation between states is interpreted as temporal precedence, while the value associated with a state is interpreted as its "real" time. We extend our proof system to be complete for TPTL, and demonstrate how it can be used to derive realtime properties.
An Integrated Modal Approach to Rational Agents
, 1997
"... In this paper we give an overview of work we have done to provide a framework in which many aspects of rational agency are integrated. The various attitudes of a rational agent, viz. the informational as well as the motivational ones, are modelled in the framework by means of a variety of modal oper ..."
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Cited by 21 (1 self)
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In this paper we give an overview of work we have done to provide a framework in which many aspects of rational agency are integrated. The various attitudes of a rational agent, viz. the informational as well as the motivational ones, are modelled in the framework by means of a variety of modal operators that are interpreted by means of possible worlds, as usual in modal logic. A main point here is that we incorporate all these modal operators into one model, so that in principle the various modal operators can be mixed to describe an agent's complex attitudes. 1 Introduction We present a single formal framework for describing crucial aspects of rational or intelligent agents. Before proposing such a formal framework, let us try and distinguish some of its necessary features in a more informal way. An essential feature of being an agent is that it has access to a variety of actions ; by using the adjective rational , we mean that the agent is able to reason. Obviously there is an inte...
Temporal Logic with Reference Pointers
 Proceedings of the 1st International Conference on Temporal Logic, volume 827 of LNAI
"... An extension of the propositional temporal language is introduced with a simple syntactic device, called "reference pointer" which provides for making references within a formula to "instants of reference" specified in the formula. The language with reference pointers L_trp has a great expressive po ..."
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Cited by 12 (1 self)
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An extension of the propositional temporal language is introduced with a simple syntactic device, called "reference pointer" which provides for making references within a formula to "instants of reference" specified in the formula. The language with reference pointers L_trp has a great expressive power (e.g. Kamp's and Stavi's operators as well as Prior's clock variables are definable in it), especially compared to its frugal syntax, perspicuous semantics and simple deductive system. The minimal temporal logic K_trp of this language is axiomatized and strong completeness theorem is proved for it and extended to an important class of extensions of K_trp . The validity in L_trp is proved undecidable.
A Logic of Capabilities
 3rd Intl Symposium on the Logical Foundations of Computer Science (LFCS 94
, 1993
"... In this paper a logic of capabilities is introduced. We start by defining a language L in which not only knowledge and actions of a set of agents can be expressed but also their abilities. To formalize the planning of the agents a Canpredicate and a Cannotpredicate are used. The former indicates t ..."
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Cited by 10 (0 self)
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In this paper a logic of capabilities is introduced. We start by defining a language L in which not only knowledge and actions of a set of agents can be expressed but also their abilities. To formalize the planning of the agents a Canpredicate and a Cannotpredicate are used. The former indicates that an agent knows that he can achieve a given goal by performing a given action, the latter indicates that the agent knows that he cannot achieve the given goal by performing the given action. We will define two classes of models, of which one is a restricted version of the other. Using these classes a semantics for the language L is defined. For the second class of models a sound and complete axiomatization is given. We define the notion of action transformation, a function that transforms actions into other actions. The semantics that we define is such that two actions that can be transformed into one another have equivalent results and that the abilities of an agent are closed under the ...
A Temporal Trace Language for Formal Modelling and Analysis of Agent Systems
"... Abstract This chapter presents the hybrid Temporal Trace Language (TTL) for formal specification and analysis of dynamic properties of multiagent systems. This language supports specification of both qualitative and quantitative aspects, and subsumes languages based on differential equations and te ..."
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Cited by 6 (4 self)
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Abstract This chapter presents the hybrid Temporal Trace Language (TTL) for formal specification and analysis of dynamic properties of multiagent systems. This language supports specification of both qualitative and quantitative aspects, and subsumes languages based on differential equations and temporal logics. TTL has a high expressivity and normal forms that enable automated analysis. Software environments for performing verification of TTL specifications have been developed. TTL proved its value in a number of domains. 1
A Complete Epistemic Logic for Multiple Agents: Combining Distributed and Common Knowledge
 Epistemic Logic and the Theory of Games and Decisions
, 1996
"... We give one overall system for describing the knowledge in a group of m agents, in which distributed knowledge, everybody's knowledge and common knowledge can be dealt with at the same time. The canonical model for this complete epistemic logic for m agents appears to lack two desirable properti ..."
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Cited by 6 (1 self)
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We give one overall system for describing the knowledge in a group of m agents, in which distributed knowledge, everybody's knowledge and common knowledge can be dealt with at the same time. The canonical model for this complete epistemic logic for m agents appears to lack two desirable properties. We combine several validitypreserving techniques to transfer the satisfiability of an epistemic formula between classes of models; thus eventually proving completeness for the logic under consideration with respect to the class of models containing all the desired properties.
Definability, Canonical Models, Compactness for Finitary Coalgebraic Modal Logic
, 2007
"... This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours ..."
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Cited by 5 (3 self)
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This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.
Seeing is Believing  And so are Hearing and Jumping
 in: Lecture Notes in Artificial Intelligence
, 1995
"... In this paper a formal framework is proposed in which various informative actions are combined, corresponding to the different ways in which rational agents can acquire information. In order to solve the various conflicts that could possibly occur when acquiring information from different sources, w ..."
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Cited by 4 (0 self)
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In this paper a formal framework is proposed in which various informative actions are combined, corresponding to the different ways in which rational agents can acquire information. In order to solve the various conflicts that could possibly occur when acquiring information from different sources, we propose a classification of the information that an agent possesses according to credibility. Based on this classification, we formalize what it means for agents to have seen or heard something, or to believe something by default. We present a formalization of observations, communication actions, and the attempted jumps to conclusions that constitutes default reasoning. To implement these informative actions we use a general belief revision action which satisfies the AGM postulates; dependent on the credibility of the incoming information this revision action acts on one or more parts of the classified belief sets of the agents. The abilities of agents formalize both the limited capacities...
Temporal Logics of Computations  Introductory Course
 th European Summer School in Logic, Language and Information
, 2000
"... representation of models for branching time logics . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.4 The computation tree logic CTL . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4.1 Complete axiomatic system for CTL. . . . . . . . . . . . . . . . . 53 4.5 Decidability and complexity of ..."
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representation of models for branching time logics . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.4 The computation tree logic CTL . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4.1 Complete axiomatic system for CTL. . . . . . . . . . . . . . . . . 53 4.5 Decidability and complexity of CTL and CTL* . . . . . . . . . . . . . . . . 54 5 Temporal logics and automata 55 5.1 Preliminaries: finite state automata . . . . . . . . . . . . . . . . . . . . . . 56 5.2 Buchi automata on infinite words . . . . . . . . . . . . . . . . . . . . . . . 57 5.3 Automata on infinite words and linear time temporal logic . . . . . . . . . . 58 5.4 Buchi automata on infinite trees . . . . . . . . . . . . . . . . . . . . . . . . 60 5.5 Automata on infinite trees and CTL . . . . . . . . . . . . . . . . . . . . . . 61 6