Semantics/Sémantique in areas (2024-02-10)

To reason and talk about the world, agents may use their own distinct vocabularies, structured into knowledge representations, also called ontologies. In order to communicate, they use alignments: translations between terms of their ontologies. aHowever, ontologies may change, requiring their alignments to evolve accordingly. Experimental cultural evolution offers a framework to study the mechanisms of their knowledge evolution. It has been applied to the evolution of alignments in the Alignment Repair Game (ARG). Experiments have shown that, through ARG, agents improve their alignments and reach successful communication. Yet, these experiments are not sufficient to understand the formal properties of cultural knowledge evolution. This thesis bridges experimental cultural knowledge evolution with a theoretical model of cultural knowledge evolution in logic. This is achieved by introducing Dynamic Epistemic Ontology Logic and defining a faithful translation of ARG in DEOL that (a) encodes the ontologies, (b) maps agents' ontologies and alignments to knowledge and beliefs, and (c) captures the adaptation operators through announcements and conservative upgrades. This model shows that all but one adaptation operator are correct, they are incomplete and some are partially redundant. Three differences between the ARG agents and their logical model explain these results, leading to an independent model of awareness based on partial valuations and weakly reflexive relations. An alternative model of ARG is then defined under which the formal properties are re-examined, showing that this model is closer to the original game. This is a first step towards defining a theoretical model of cultural knowledge evolution.

The paradigm of algebraic constraint-based reasoning, embodied in the notion of a qualitative calculus, is studied within two alternative frameworks. One framework defines a qualitative calculus as "a non-associative relation algebra (NA) with a qualitative representation", the other as "an algebra generated by jointly exhaustive and pairwise disjoint (JEPD) relations". These frameworks provide complementary perspectives: the first is intensional (axiom-based), whereas the second one is extensional (based on semantic structures). However, each definition admits calculi that lie beyond the scope of the other. Thus, a qualitatively representable NA may be incomplete or non-atomic, whereas an algebra generated by JEPD relations may have non-involutive converse and no identity element. The divergence of definitions creates a confusion around the notion of a qualitative calculus and makes the "what" question posed by Ligozat and Renz actual once again. Here we define the relation-type qualitative calculus unifying the intensional and extensional approaches. By introducing the notions of weak identity, inference completeness and Q-homomorphism, we give equivalent definitions of qualitative calculi both intensionally and extensionally. We show that "algebras generated by JEPD relations" and "qualitatively representable NAs" are embedded into the class of relation-type qualitative algebras.

Partial Dynamic Epistemic Logic allows agents to have different knowledge representations about the world through agent awareness. Agents use their own vocabularies to reason and talk about the world and raise their awareness when confronted with new vocabulary. Through raising awareness the vocabularies of agents are extended, suggesting there is a dual, inverse operator for forgetting awareness that decreases vocabularies. In this paper, we discuss such an operator. Unlike raising awareness, this operator may induce an abstraction on models that removes evidence while preserving conclusions. This is useful to better understand how agents with different knowledge representations communicate with each other, as they may forget the justifications that led them to their conclusions.