A Formal Model of Metaphor in Frame Semantics

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics

Computational and Robotic Models of Early Language Development: A Review

We review computational and robotics models of early language learning and development. We first explain why and how these models are used to understand better how children learn language. We argue that they provide concrete theories of language learning as a complex dynamic system, complementing traditional methods in psychology and linguistics. We review different modeling formalisms, grounded in techniques from machine learning and artificial intelligence such as Bayesian and neural network approaches. We then discuss their role in understanding several key mechanisms of language development: cross-situational statistical learning, embodiment, situated social interaction, intrinsically motivated learning, and cultural evolution. We conclude by discussing future challenges for research, including modeling of large-scale empirical data about language acquisition in real-world environments. Keywords: Early language learning, Computational and robotic models, machine learning, development, embodiment, social interaction, intrinsic motivation, self-organization, dynamical systems, complexity.Comment: to appear in International Handbook on Language Development, ed. J. Horst and J. von Koss Torkildsen, Routledg

Translating and Evolving: Towards a Model of Language Change in DisCoCat

The categorical compositional distributional (DisCoCat) model of meaning developed by Coecke et al. (2010) has been successful in modeling various aspects of meaning. However, it fails to model the fact that language can change. We give an approach to DisCoCat that allows us to represent language models and translations between them, enabling us to describe translations from one language to another, or changes within the same language. We unify the product space representation given in (Coecke et al., 2010) and the functorial description in (Kartsaklis et al., 2013), in a way that allows us to view a language as a catalogue of meanings. We formalize the notion of a lexicon in DisCoCat, and define a dictionary of meanings between two lexicons. All this is done within the framework of monoidal categories. We give examples of how to apply our methods, and give a concrete suggestion for compositional translation in corpora.Comment: In Proceedings CAPNS 2018, arXiv:1811.0270

Formal logic: Classical problems and proofs

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational

Apperceptive patterning: Artefaction, extensional beliefs and cognitive scaffolding

In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog)