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Knowledge without Modality: A Simplified Framework for Chronological Ignorance
 Logics in AI: Proc. 3rd European Workshop on Logics in Artificial Intelligence
, 1992
"... . Shoham's logic of chronological ignorance (CI) provides a formal approach for representing and reasoning about causal relationships. The utility of the formalism comes from imposing a partial order on Kripke interpretations for theories in a modal logic of temporal knowledge. In this paper we show ..."
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. Shoham's logic of chronological ignorance (CI) provides a formal approach for representing and reasoning about causal relationships. The utility of the formalism comes from imposing a partial order on Kripke interpretations for theories in a modal logic of temporal knowledge. In this paper we show that the use of modal logic in this context is unnecessary and that the same result can be achieved using classical logic. While semantically simpler, the classical approach is somewhat unwieldy. To overcome this problem we suggest an alternative underlying language, called asserted logic. The logic allows the convenient representation found in Shoham's approach without sacrificing the truth functional semantics and proof theory of classical logic. We demonstrate the utility of the logic by providing an equivalent nonmodal CI framework for causal theories. 1 Introduction The logic of chronological ignorance (CI) [15, 16] was proposed by Shoham as a solution to the qualification and extende...
A Practical Theory of Nonmonotonic Temporal Modelling
 Proceedings of AAAI94 Workshop on Spatial and Temporal Reasoning Seattle, Washington pp
, 1994
"... This paper sets out a framework for modelling causal or predictive systems, and is concerned with bridging the gap between the theory and practice of nonmonotonic temporal reasoning. The central result is a nonmonotonic reasoning methodology which subsumes Shoham's chronological ignorance (CI) forma ..."
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This paper sets out a framework for modelling causal or predictive systems, and is concerned with bridging the gap between the theory and practice of nonmonotonic temporal reasoning. The central result is a nonmonotonic reasoning methodology which subsumes Shoham's chronological ignorance (CI) formalism for causal theories. The new formalism uses an extension of Reiter 's default logic and, unlike chronological ignorance, the approach is prooftheoretic. This leads to a simple proof procedure based on classical deduction. We suggest several improvements over Shoham's approach which include removing the need for a modal (or other epistemic) logic. The result is a simple framework for predictive modelling which can be implemented using a standard theorem prover. Keywords: causal reasoning, nonmonotonic temporal reasoning, predictive modelling, default logic 1 Introduction Formal techniques for modelling systems characterised by discrete events have failed to attract the confidence and...
Building Models of Prediction Theories
 In
, 1998
"... This paper is concerned with the implementation of Prediction Theories. Rather than developing and then attempting to implement a proof theory, it aims instead to implement their model theory by building computational counterparts of their relevant models. Prediction Theories are outlined and ..."
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This paper is concerned with the implementation of Prediction Theories. Rather than developing and then attempting to implement a proof theory, it aims instead to implement their model theory by building computational counterparts of their relevant models. Prediction Theories are outlined and examples involving inertia, qualifications, ramifications and concurrency are given. The basic modelbuilding algorithm is then presented and its completeness and correctness is proved. Several extensions to this algorithm are then outlined. Finally, the performance of the algorithms is analysed. 1 Introduction This paper is concerned with the implementation of Prediction Theories (PTs) (Bell, 1997). PTs were developed to represent predictive common sense causal reasoning. In particular they provide a modeltheoretic means of representing inertia, ramifications, qualifications, simultaneity, and nondeterminism. Rather than developing and then attempting to implement a proof theory f...