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Reports (Research Report) Year : 2022

Theory Synthesis based on Experience

Synthèse de Théorie Basée sur l'Expérience


We present in this report a novel approach to learning that results in a first-order logic model. The construction proceeds in two steps. In the first step we interpret first-order function symbols as strict Scott-continuous functions over algebraic domains, a category that encompasses among others sets of traces and sets of sets. First-order terms are composition of functions, and a ``flight envelope'' of the system is constructed through the construction of new terms and the recording of the maximal values encountered for the terms during the analysis of a set of traces. We prove that this approach has an Angluin-like property for learning with respect to false positives and negatives. This approach is also practical and was applied in previous works to construct efficient intrusion detection systems. In the second step we consider an ordered set of cognitive states. Each cognitive state is a representation model equiped with a set of ground object terms denoting the facts on which reasoning is based and a set of representation terms denoting the tests performed on these object terms. Under an additional condition of stability we construct for each cognitive state a set of predicates over a constructed domain such that elements of the domains are the equivalence classes of the object terms relative to the predicates while predicates are defined by sets of object terms. We prove that the ordered set of models derived from the cognitive states forms an inverse system of first-order logic model. This construction fills the gap in previous work by Achourioti and van Lanbalgem were inverse systems of first-order logic models are employed to formalize Kant's approach to reasoning in the Critique of the Pure Reason.
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Dates and versions

hal-03829757 , version 1 (25-10-2022)
hal-03829757 , version 2 (23-01-2023)


  • HAL Id : hal-03829757 , version 2


Yannick Chevalier. Theory Synthesis based on Experience. [Research Report] IRIT/RR–2022–08–FR, IRIT - Institut de Recherche en Informatique de Toulouse. 2022. ⟨hal-03829757v2⟩
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