Ethics in the flesh: formalizing moral values in embodied cognition

Values are beliefs or principles that are deemed significant or desirable within a specific society or culture, serving as the fundamental underpinnings for ethical and socio-behavioral norms. The objective of this research is to explore the domain encompassing moral, cultural, and individual values. To achieve this, we employ an ontological approach to formally represent the semantic relations within the value domain. The theoretical framework employed adopts Fillmore’s frame semantics, treating values as semantic frames. A value situation is thus characterized by the co-occurrence of specific semantic roles fulfilled within a given event or circumstance. Given the intricate semantics of values as abstract entities with high social capital, our investigation extends to two interconnected domains. The first domain is embodied cognition, specifically image schemas, which are cognitive patterns derived from sensorimotor experiences that shape our conceptualization of entities in the world. The second domain pertains to emotions, which are inherently intertwined with the realm of values. Consequently, our approach endeavors to formalize the semantics of values within an embodied cognition framework, recognizing values as emotional-laden semantic frames. The primary ontologies proposed in this work are: (i) ValueNet, an ontology network dedicated to the domain of values; (ii) ISAAC, the Image Schema Abstraction And Cognition ontology; and (iii) EmoNet, an ontology for theories of emotions. The knowledge formalization adheres to established modeling practices, including the reuse of semantic web resources such as WordNet, VerbNet, FrameNet, DBpedia, and alignment to foundational ontologies like DOLCE, as well as the utilization of Ontology Design Patterns. These ontological resources are operationalized through the development of a fully explainable frame-based detector capable of identifying values, emotions, and image schemas generating knowledge graphs from from natural language, leveraging the semantic dependencies of a sentence, and allowing non trivial higher layer knowledge inferences.

Towards a logical foundation of randomized computation

This dissertation investigates the relations between logic and TCS in the probabilistic setting. It is motivated by two main considerations. On the one hand, since their appearance in the 1960s-1970s, probabilistic models have become increasingly pervasive in several fast-growing areas of CS. On the other, the study and development of (deterministic) computational models has considerably benefitted from the mutual interchanges between logic and CS. Nevertheless, probabilistic computation was only marginally touched by such fruitful interactions. The goal of this thesis is precisely to (start) bring(ing) this gap, by developing logical systems corresponding to specific aspects of randomized computation and, therefore, by generalizing standard achievements to the probabilistic realm. To do so, our key ingredient is the introduction of new, measure-sensitive quantifiers associated with quantitative interpretations. The dissertation is tripartite. In the first part, we focus on the relation between logic and counting complexity classes. We show that, due to our classical counting propositional logic, it is possible to generalize to counting classes, the standard results by Cook and Meyer and Stockmeyer linking propositional logic and the polynomial hierarchy. Indeed, we show that the validity problem for counting-quantified formulae captures the corresponding level in Wagner's hierarchy. In the second part, we consider programming language theory. Type systems for randomized \lambda-calculi, also guaranteeing various forms of termination properties, were introduced in the last decades, but these are not "logically oriented" and no Curry-Howard correspondence is known for them. Following intuitions coming from counting logics, we define the first probabilistic version of the correspondence. Finally, we consider the relationship between arithmetic and computation. We present a quantitative extension of the language of arithmetic able to formalize basic results from probability theory. This language is also our starting point to define randomized bounded theories and, so, to generalize canonical results by Buss.