This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

In this paper we analyse the conditions for attributing to AI autonomous systems the ontological status of “artificial moral agents”, in the context of the “distributed responsibility” between humans and machines in Machine Ethics (ME). In order to address the fundamental issue in ME of the unavoidable “opacity” of their decisions with ethical/legal relevance, we start from the neuroethical evidence in cognitive science. In humans, the “transparency” and then the “ethical accountability” of their actions as responsible moral agents is not (...) in contradiction with the unavoidable “opacity” (unawareness) of the brain process by which they perform their moral judgements on the right action to execute. In fact, the moral accountability of our actions depends on what is immediately before and after our “moral judgements” on the right action to execute (formally, deontic first order logic (FOL) decisions). I.e., our moral accountability depends on the “ethical constraints” we imposed to our judgement before performing it in an opaque way. Anyway, our moral accountability depends overall on the “ethical assessment” or explicit “moral reasoning” after and over the moral judgement before executing our actions (deontic higher order logic (HOL) assessment). In this way, in the light of the AI “imitation game”, the consistent attribution of the status of ethically accountable artificial moral agents to autonomous AI systems depends on two similar conditions. Firstly, it depends on the presence of “ethical constraints” to be satisfied in their Machine Learning (ML) supervised optimization algorithm during its training phase, to give the system ethical skills (“competences”) in its decisions. Secondly – and definitely—, it depends on the presence in an AI autonomous system of a deontic HOL “ethical reasoner” to perform an automatic, and fully transparent assessment (metalogical deontic valuation) about the decisions taken by the ethically skilled ML algorithm about the right action to execute, before executing it. Finally, we show that the proper deontic FOL and HOL for this class of artificial moral agents is Kripke’s modal relational logic, in its algebraic topological formalization. This is naturally implemented in the dissipative QFT unsupervised deep learning of our brains, based on the “doubling of the degrees of freedom” (DDF), and then in the so-called “deep-belief” artificial neural networks for the statistical data pre-processing. This unsupervised learning procedure is also compliant with the usage of the “maximin fairness principle”, used as a balancing aggregation principle of the statistical variables in Sen’s formal theory of fairness. (shrink)

This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both (...) of the “extensional” logics of the pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences. (shrink)

This is a collection of new investigations and discoveries on the theory of opposition by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum system and its inseparable thermal bath, formally “entangled” like (...) an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions. (shrink)

In Posner & Raichle's (1994) book, two essential and strictly related limitations of cognitive neurophysiology are not sufficiently enhanced: (1) The problem of “coding,” namely the capability of a natural brain to redefine its own “basic symbols” as a function of a changing environment; (2) the inadequacy of a Hebbian rule to reckon with complex computational problems such as those solved by real brains.