Knowledge representation and automated reasoning are two of the pillars of Artificial Intelligence but, differently from other pillars, they are strictly intertwined. Depending on how knowledge is represented, different types of reasoning can be applied and, on the other hand, new developments in the automated reasoning column fosters new ideas on the knowledge representation side. The Italian community has been always very involved in these fascinating themes, and this is witnessed by the lively group of knowledge representation and automated reasoning (Rappresentazione della Conoscenza e Ragionamento Automatico, RCRA) of AI*IA. In this paper we survey the developments on automated reasoning in the last 25 years, with particular emphasis on the research of the Italian community and of the RCRA group. The focus will be mainly on the algorithmic side, while a companion paper focuses more on the knowledge representation side, and on the vast area of semantic technologies.
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