A Description Logic for Analogical Reasoning

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more widespread adoption. To mitigate this issue, we present a mechanism to infer plausible missing knowledge, which relies on reasoning by analogy. To the best of our knowledge, this is the first paper that studies analogical reasoning within the setting of description logic ontologies. After showing that the standard formalisation of analogical proportion has important limitations in this setting, we introduce an alternative semantics based on bijective mappings between sets of features. We then analyse the properties of analogies under the proposed semantics, and show among others how it enables two plausible inference patterns: rule translation and rule extrapolation.

Algorithmic definitions for KLM-style defeasible disjunctive Datalog

Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach for extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure. We provide algorithmic definitions for these forms of defeasible entailment and prove that the definitions are LM-rational.

¬Peirce’s Creative Hallucinations in the Ontogeny of Abductive Reasoning

This inquiry proposes that Peirce’s ultimate concept of dreams, which can be sub-divided in seven different functions, supply the raw material for habit-change inherent in every plausible inference. With references to developmental literature, I propose that dreams represent an outlet whereby children rely upon vivid directional icons of events (virtual habits) in reconciling logical anomalies provoked by unexpected happenings. Accordingly, dreams supply insights into how potential happenings materialize – identifying which factors can enhance/enrich the effectiveness of potential event outcomes. Dreams of this creative kind are not obsessional or socially driven but rather form the bedrock for conceiving of many meritorious insights, as shown in phenomena like children’s prelinguistic habits, word substitutions, overextensions, role-play and perspective taking.

II Old Comedy and Aristophanes

Although the competition for comedies at the Athenian City Dionysia was made official in 486, the genre itself is certainly older, probably by generations. In this much-discussed passage from the Poetics, Aristotle complains that his research into the early history of Attic drama was hampered in the case of comedy by a shortage of documentation, making it impossible to construct the kind of developmental history that he was able to piece together for tragedy. Only with the generation of Crates, whose career began around 450, did a clear sequence of innovation start to become traceable, and for the earlier period Aristotle himself seems to have been driven back on what would have appeared to him a plausible inference: that comedy had evolved in the same way as tragedy, from a pre-dramatic mode of performance through the separation of chorus and soloist. He saw a credible ancestor in the phallic songs’ performed at Dionysiac festivals around Attica, such as the one staged in Acharnians (237 ff.), and suggested that the lead voice in such processional songs (taken by Dicaeopolis in the Acharnians scene) was the origin of the comic solo actor.