Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure

Vector Semantics

This open access book introduces Vector semantics, which links the formal theory of word vectors to the cognitive theory of linguistics. The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use. In spite of the fact that these two schools both have ‘linguistics’ in their name, so far there has been very limited communication between them, as their historical origins, data collection methods, and conceptual apparatuses are quite different. Vector semantics bridges the gap by presenting a formal theory, cast in terms of linear polytopes, that generalizes both word vectors and conceptual structures, by treating each dictionary definition as an equation, and the entire lexicon as a set of equations mutually constraining all meanings

Vector Semantics

This open access book introduces Vector semantics, which links the formal theory of word vectors to the cognitive theory of linguistics. The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use. In spite of the fact that these two schools both have ‘linguistics’ in their name, so far there has been very limited communication between them, as their historical origins, data collection methods, and conceptual apparatuses are quite different. Vector semantics bridges the gap by presenting a formal theory, cast in terms of linear polytopes, that generalizes both word vectors and conceptual structures, by treating each dictionary definition as an equation, and the entire lexicon as a set of equations mutually constraining all meanings