Abstract. We present a framework for characterizing spike (and spiketrain) synchrony in parallel neuronal spike trains that is based on identifying spikes with what we call influence maps: real-valued functions describing an influence region around the corresponding spike times within which possibly graded synchrony with other spikes is defined. We formalize two models of synchrony in this framework: the bin-based model (the almost exclusively applied model in the literature) and a novel, alternative model based on a continuous, graded notion of synchrony, aimed at overcoming the drawbacks of the bin-based model. We study the task of identifying frequent (and synchronous) neuronal patterns from parallel spike trains in our framework, formalized as an instance of what we call the fuzzy frequent pattern mining problem (a generalization of standard frequent pattern mining) and briefly evaluate our synchrony models on this task.

CADIAG-2 is a well-known expert system aimed at providing support for medical diagnose in the field of internal medicine. CADIAG-2 consists of a knowledge base in the form of a set of IF-THEN rules that relate distinct medical entities, in this paper interpreted as conditional probabilistic statements, and an inference engine constructed upon methods of fuzzy set theory. The aim underlying this paper is the understanding of the logical structure of the inference in CADIAG-2. To that purpose, we provide a (probabilistic) logical formalisation of the inference of the system and check its adequacy with probabilistic logic.Keywords Knowledge-based systems Á Rule-based expert systems Á Fuzzy expert systems Á Probabilistic inference Á CADIAG-2

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CADIAG-2 is a well known rule-based medical expert system aimed at providing support in medical diagnose in the field of internal medicine. Its knowledge base consists of a large collection of IF-THEN rules that represent uncertain relationships between distinct medical entities. Given this uncertainty and the size of the system, it has been challenging to validate its consistency. Recent attempts to partially formalize CADIAG-2’s knowledge base into decidable Gödel logics have shown that, on formalization, the system is inconsistent. In this paper, the authors use an alternative, more expressive formalization of CADIAG-2’s knowledge base as a set of probabilistic conditional statements and apply their probabilistic logic solver (Pronto) to confirm its inconsistency and compute its conflicting sets of rules under a slightly relaxed interpretation. Once this is achieved, the authors define a measure to evaluate inconsistency and discuss suitable repair strategies for CADIAG-2 and similar systems.