Marco Giunti

This paper critically examines the recent publication “ChatGPT-4 in the Turing Test” by Restrepo Echavarría (Minds Mach 35:8, 2025. https://doi.org/10.1007/s11023-025-09711-6), challenging its central claims regarding the absence of minimally serious test implementations and the conclusion that ChatGPT-4 fails the Turing Test. The analysis reveals that the criticisms based on rigid criteria and limited experimental data are not fully justified. More importantly, the paper makes several constructive contributions that enrich our understanding of Turing Test implementations. It demonstrates that two distinct formats, the three-player and two-player tests, are both valid, each with unique methodological implications. The work distinguishes between absolute criteria for passing the test—the machine’s probability of incorrect identification equals or exceeds the human’s probability of correct identification—and relative criteria—which measure how closely a machine’s performance approximates that of a human—, offering a more nuanced evaluation framework. Furthermore, the paper clarifies the probabilistic underpinnings of both test types by modeling them as Bernoulli experiments—correlated in the three-player version and uncorrelated in the two-player version. This formalization allows for a rigorous separation between the theoretical criteria for passing the test, defined in probabilistic terms, and the experimental data that require robust statistical methods for proper interpretation. In doing so, the paper not only refutes key aspects of the criticized study but also lays a solid foundation for future research on objective measures of how closely an AI’s behavior aligns with, or deviates from, that of a human.

The human mind is constantly engaged in predicting the future using past experiences to anticipate what is likely to happen next. The predictive coding approach focuses on this ongoing activity and proposes a unified mechanism that underlies both perception and action. In this paper, we show that some applications of the predictive coding model to memory and perception processes often face the ambiguity of two controversial aspects. (I) How can the brain apply similar mechanisms to handle qualitatively different degrees of prediction (e.g. imaginative and procedural predictions)? (II) How is it possible to reconcile the presence of stable mental representations with the continuous dynamic change of perceptual data? We suggest that the relation between different degrees of prediction can be seen as analogous to the relation between a perception and its recollection, and we argue that this relation can be better understood within a timing-based approach that looks at the temporal architectures underlying these cognitive phenomena. Therefore, based on the interpretation of some empirical data from the study of auditory perception, we show how the timing-based approach we delineate can help to clarify aspects (I) and (II).

In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections.

In this paper we argue that the debate between representational and anti-representational cognitive theories cannot be reduced to a difference between the types of model respectively employed. We show that, on the one side, models standardly used in representational theories, such as computational ones, can be analyzed in the context of dynamical systems theory and, on the other, non-representational theories such as Gibson’s ecological psychology can be formalized with the use of computational models. Given these considerations, we propose that the true conceptual difference between representational and anti-representational cognitive descriptions should be characterized in terms of style of explanation, which indicates the particular stance taken by a theory with respect to its explanatory target.

The vision underlying the development of the Semantic Web is that the whole complex of our knowledge forms a huge semantic network, which should be represented and made explicit by means of languages such as RDF, RDFS or OWL. However, these languages have important expressive limits, since none of them reaches the full expressive power of a first-order language. As a result, large parts of our knowledge—in particular, mathematical and scientific theories—cannot currently be made available on the Semantic Web as linked data, not even in principle. In this work, we are going to define FOOL (first-order ontology language), a new ontological language compatible with RDF, which allows the expression of any formula of a first-order language as a connected RDF graph. FOOL is as expressive as a first-order language, but unlike it, its statements do not have a serialized form. Instead, like a RDF statement, each statement of a FOOL knowledge base is a connected graph, and different statements link to each other through the meaningful nodes they share. In this way, the semantic relationships between statements are made explicit, and given FOOL’s compatibility with RDF, virtually the entire complex of our knowledge can in principle be made available on the Semantic Web as linked data. The semantic relationships made explicit by a FOOL ontology are not those of logical consequence, but they are meaning connections between statements represented as graphs. It is not far-fetched to think that, by devising appropriate measures of the linking patterns between statements, such relations can be mechanized, thus opening the way to new and possibly unforeseen results and applications.

Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show how this model gives rise to a new ontological pattern (parametric pattern) for the representation of such relations in the Semantic Web. To this end, we define PROL (Parametric Relational Ontology Language). PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided.

In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections.

The received view on the problem of the direction of time holds it that time has no intrinsic dynamical properties, and that its apparent asymmetry, to be understood in purely topological terms, is dependent on the directional properties of physical processes. In this paper we shall challenge both claims, in the light of an algebraic representation of time. First, we will show how to give a precise formulation to the intuitive idea that time possesses an intrinsic dynamics; this formulation relies on the fact that the algebraic properties of time can equivalently be understood in dynamical terms. Second, we shall argue that the directional properties displayed by the processes occurring in time depend on the directional properties of time, rather than the converse.

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed.

According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is sufficient for reduction. I then extend this representational model-based view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction

Il lavoro esamina criticamente i presupposti di cinque differenti approcci alla Scienza Cognitiva, (simbolico, connessionista, dinamico, della cognizione incarnata e della vita artificiale) e sostiene che tutti e cinque condividono tacitamente un’ipotesi metodologica molto generale. Tale ipotesi, che propongo di chiamare simulazionismo , postula che i fenomeni cognitivi di un qualunque sistema reale possono essere adeguatamente spiegati sulla base di opportuni modelli di simulazione del sistema stesso. Tuttavia, a causa della loro costituzione, i modelli di simulazione hanno forti limitazioni, sia al livello descrittivo che esplicativo. Il limite descrittivo sta nel fatto che la corrispondenza fra i risultati di una simulazione e i dati relativi al fenomeno reale non è diretta e intrinseca ma, al più, indiretta e estrinseca. Il limite esplicativo consiste nel fatto che le spiegazioni supportate dal modello non sono mai compiute e realistiche ma, piuttosto, solo in linea di principio e romanzesche. Queste difficoltà potrebbero essere superate ricorrendo ai modelli Galileiani , costituiti da sistemi dinamici in cui ciascuna componente ha un’interpretazione precisa e definita, in quanto essa corrisponde ad una proprietà misurabile (grandezza) del fenomeno reale che il modello descrive

The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamical systems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical system DS2 when DS1 exactly reproduces the whole dynamics of DS2). This representational view of reduction, contrary to the standard deductivist one, is compatible with the existence of structural properties of the reduced system that are not also properties of the reducing one. Therefore, under this view, by no means are reduction and emergence incompatible categories but, rather, complementary ones.

This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of dynamical systems, which I call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories