Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence

The new computational paradigm of conceptual computation has been introduced in the research program of Artificial Mathematical Intelligence. We provide the explicit artificial generation (or conceptual computation) for the fundamental mathematical notion of topological groups. Specifically, we start with two basic notions belonging to topology and abstract algebra, and we describe recursively formal specifications in the Common Algebraic Specification Language (CASL). The notion of conceptual blending between such conceptual spaces can be materialized computationally in the Heterogeneous Tool Set (HETS). The fundamental notion of topological groups is explicitly generated through three different artificial specifications based on conceptual blending and conceptual identification, starting with the concepts of continuous functions and mathematical groups (described with minimal set-theoretical conditions). This constitutes in additional heuristic evidence for the third pillar of Artificial Mathematical Intelligence.

Towards a General Many-Sorted Framework for Describing Certain Kinds of Legal Statutes with a Potential Computational Realization

Examining a 20th-century Scandinavian legal theoretical tradition, we can extract an ontological naturalistic, a logical empiristic, and a modern idealistic rationale. We introduce the mathematical syntactic figure present in the `logical empiricism' in a contemporary mathematical logic. A new formal framework for describing explicit purchase statutes (Sweden) is gradually developed and subsequently proposed. This new framework is based on a many-sorted first-order logic (MFOL) approach, where the semantics are grounded in concrete `physical' objects and situations with a legal relevance. Specifically, we present a concrete formal syntactic translation of one of the central statutes of Swedish legislation for the purchase of immovable property. Additionally, we discuss the potential implications that a subsequent development of such formalisations would have for constructing artificial agents (e.g., software) that can be used as `co-creative' legal assistance for solving highly complex legal issues concerning the transfer of property, among others.

Some Pragmatic Prevention's Guidelines regarding SARS-CoV-2 and COVID-19 in Latin-America inspired by mixed Machine Learning Techniques and Artificial Mathematical Intelligence. Case Study: Colombia

We use an enhanced methodology combining specific forms of AI techniques, opinion mining and artificial mathematical intelligence (AMI), with public data on the spread of the coronavirus SARS-CoV-2 and the incidence of COVID-19 disease in Colombia during the first three months since the first reported positive case. The results obtained, together with conceptual tools coming from the global taxonomy of fundamental cognitive mechanisms emerging in AMI and with suitable contextual information from Colombian public health and mainstream social media, allowed us to stating specific preventive guidelines for a better restructuring of initial safe and stable life conditions in Colombia, and in an extended manner in similar Latin American Countries. More specifically, we describe three major guidelines: 1) regular creative visualization and effective planning, 2) the continuous use of constructive linguistic frameworks, and 3) frequent and moderate use of kinesthetic routines. They should be understood as effective tools from a cognitive and behavioural perspective, rather than from a biological one. Even more, the first two guidelines should be acknowledged in integral cooperation with the third one regarding the global effect of COVID-19 in human beings as a whole, this includes the mind and body.