We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in (...) a definable way, thus providing a sort of “canonical” set of values for the functional representation. (shrink)

In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.

Formulas of n variables of Łukasiewicz sentential calculus can be represented, via McNaughton’s theorem, by piecewise linear functions, with integer coefficients, from hypercube [0,1] n to [0,1], called McNaughton functions. As a consequence of the McNaughton representation of a formula it is obtained a canonical form of a formula. Indeed, up to logical equivalence, any formula can be written as an infimum of finite suprema of formulas associated to McNaughton functions which are truncated functions to $[0,1]$ of the (...) restriction to [0,1] n of single hyperplanes, for short, called simple McNaughton functions. In the present paper we will concern with the problem of presenting formulas of Lukasiewicz sentential calculus in normal form. Here we list the main results we obtained: a) we give an axiomatic description of some classes of formulas having the property to be canonically mapped one-to-one onto the class of simple Mc Naughton functions; b) we provide normal forms for Lukasiewicz sentential calculus, making use of formulas defined in a); c) we prove the polynomial complexity of formulas, in normal form, coming from a certain class described as in a); d) we extend the results described in a), b) and c) to Rational Lukasiewicz logic. (shrink)

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces.

We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.

It is introduced a new algebra$$(A, \otimes, \oplus, *, \rightharpoonup, 0, 1)$$(A,⊗,⊕,∗,⇀,0,1)called$$L_PG$$LPG-algebra if$$(A, \otimes, \oplus, *, 0, 1)$$(A,⊗,⊕,∗,0,1)is$$L_P$$LP-algebra (i.e. an algebra from the variety generated by perfectMV-algebras) and$$(A,\rightharpoonup, 0, 1)$$(A,⇀,0,1)is a Gödel algebra (i.e. Heyting algebra satisfying the identity$$(x \rightharpoonup y ) \vee (y \rightharpoonup x ) =1)$$(x⇀y)∨(y⇀x)=1). The lattice of congruences of an$$L_PG$$LPG-algebra$$(A, \otimes, \oplus, *, \rightharpoonup, 0, 1)$$(A,⊗,⊕,∗,⇀,0,1)is isomorphic to the lattice of Skolem filters (i.e. special type ofMV-filters) of theMV-algebra$$(A, \otimes, \oplus, *, 0, 1)$$(A,⊗,⊕,∗,0,1). The variety$$\mathbf {L_PG}$$LPGof$$L_PG$$LPG-algebras (...) is generated by the algebras$$(C, \otimes, \oplus, *, \rightharpoonup, 0, 1)$$(C,⊗,⊕,∗,⇀,0,1)where$$(C, \otimes, \oplus, *, 0, 1)$$(C,⊗,⊕,∗,0,1)is ChangMV-algebra. Any$$L_PG$$LPG-algebra is bi-Heyting algebra. The set of theorems of the logic$$L_PG$$LPGis recursively enumerable. Moreover, we describe finitely generated free$$L_PG$$LPG-algebras. (shrink)

In this paper we give a representation of the free MV-algebra over one generator as a structure of functions having finite domain.

In [9] Mundici introduced a categorical equivalence Γ between the category of MV-algebras and the category of abelian [MATHEMATICAL SCRIPT SMALL L]-groups with strong unit. Using Mundici's functor Γ, in [8] the authors established an equivalence between the category of perfect MV-algebras and the category of abelian [MATHEMATICAL SCRIPT SMALL L]-groups. Aim of the present paper is to use the above functors to provide Yosida like representations of a large class of MV-algebras.

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.

We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.

In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such state MV-algebras with the category of unital Abelian ℓ-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.

The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...) the automorphism groups of the free MV-algebras over finitely many generators. (shrink)

BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.

In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called ŁΠG.

ABSTRACT In this paper we shall prove that l-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterize l-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation between l-ideals in l-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to the f-rings.

We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \-skeleton is trivial.

The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes (...) for the future. (shrink)

Dominical categories are categories in which the notions of partial morphisms and their domains become explicit, with the latter being endomorphisms rather than subobjects of their sources. These categories form the basis for a novel abstract formulation of recursion theory, to which the present paper is devoted. The abstractness has of course its usual concomitant advantage of generality: it is interesting to see that many of the fundamental results of recursion theory remain valid in contexts far removed from their classic (...) manifestations. A principal reason for introducing this new formulation is to achieve an algebraization of the generalized incompleteness theorem, by providing a category-theoretic development of the concepts and tools of elementary recursion theory that are inherent in demonstrating the theorem.Dominical recursion theory avoids the commitment to sets and partial functions which is characteristic of other formulations, and thus allows for an intrinsic recursion theory within such structures as polyadic algebras. It is worthy of notice that much of elementary recursion theory can be developedwithout referencetoelements.By Gödel's generalized incompleteness theorem for consistent arithmetical systemTwe mean any statement of the following sort: if every recursive set is definable inT, thenTis essentially undecidable [41]; or if all recursive functions are definable inT, thenTis essentially undecidable [41]; or if every recursive set is definable inT, thenT0andR0 are recursively inseparable [39]; or if all re sets are representable inT, thenT0is creative [28], [39]; or ifTis a Rosser theory, thenT0andR0are effectively inseparable [39]. (shrink)

In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unit.

In this paper we show that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well.

We show that the complete first order theory of an MV algebra has equation image countable models unless the MV algebra is finitely valued. So, Vaught's Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are equation image and that all ω-categorical complete theories of MV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators (...) of any locally finite variety of MV algebras is ω-categorical. (shrink)

Selective retrieval of task-relevant information often facilitates memory retention of that information. However, it is still unclear if selective retrieval of task-relevant information can alter memory for task-irrelevant information, and the role of emotional arousal in it. In two experiments, we used emotional and neutral faces as stimuli, and participants were asked to memorise the name (who is this person?) and location (where does he/she come from?) associated with each face in initial study. Then, half of the studied faces were (...) presented as cues, and participants were asked to retrieve the corresponding names (Experiment 1) or locations (Experiment 2). Finally, all the faces were presented and participants were asked to retrieve both the corresponding names and locations. The results of the final test showed that retrieval practice not only enhanced memory of task-relevant information but also enhanced memory of task-irrelevant information. More importantly, negative emotion amplified the retrieval practice effect overall, with a larger retrieval-induced benefit for the negative than neutral condition. These findings demonstrated an emotional arousal amplification effect on retrieval-induced enhancement effects, suggesting that the advantage of the retrieved memory representations can be amplified by emotional arousal even without explicit goals in a task setting. (shrink)

Rousseau et l'exegese biblique du XVIIIe siecle -- Des pratiques bibliques du XVIIIe siecle a la lecture-consolation de Rousseau -- Intertextualite biblique dans l'ouvre de Rousseau -- Intertexte biblique et representation de soi -- Le Levite d'Ephraim : reecriture biblique -- Schemes de la pensee du religieux -- Ouvre de doctrine : la lettre a Christophe de Beaumont -- Etre Chretien de Jacques : les lettres ecrites de La Montagne.

The sensorimotor approach to perception addresses various aspects of perceptual experience, but not the subjectivity of intentional action. Conversely, the problem that current accounts of the sense of agency deal with is primarily one of subjectivity. But the proposed models, based on internal signal comparisons, arguably fail to make the transition from subpersonal computations to personal experience. In this paper we suggest an alternative direction towards explaining the sense of agency by braiding three theoretical strands: a world-involving, dynamical interpretation of (...) the sensorimotor approach, an enactive description of sensorimotor agency as contrasted with organic agency in general, and a dynamical theory of equilibration within and between sensorimotor schemes. On this new account, the sense of oneself as the author of one’s own actions corresponds to what we experience during the ongoing adventure of establishing, losing, and re-establishing meaningful interactions with the world. The meaningful relation between agent and world is given by the precarious constitution of sensorimotor agency as a self-asserting network of schemes and dispositions. Acts are owned as they adaptively assert the constitution of the agent. Thus, awareness for different aspects of agency experience, such as the initiation of action, the effort exerted in controlling it, or the achievement of the desired effect, can be accounted for by processes involved in maintaining the sensorimotor organization that enables these interactions with the world. We discuss these processes in detail from a non-representational, dynamical perspective and show how they cohere with the personal experience of agency. (shrink)

A novel theoretical framework for an embodied, non-representational approach to language that extends and deepens enactive theory, bridging the gap between sensorimotor skills and language. -/- Linguistic Bodies offers a fully embodied and fully social treatment of human language without positing mental representations. The authors present the first coherent, overarching theory that connects dynamical explanations of action and perception with language. Arguing from the assumption of a deep continuity between life and mind, they show that this continuity extends to language. (...) Expanding and deepening enactive theory, they offer a constitutive account of language and the co-emergent phenomena of personhood, reflexivity, social normativity, and ideality. Language, they argue, is not something we add to a range of existing cognitive capacities but a new way of being embodied. Each of us is a linguistic body in a community of other linguistic bodies. The book describes three distinct yet entangled kinds of human embodiment, organic, sensorimotor, and intersubjective; it traces the emergence of linguistic sensitivities and introduces the novel concept of linguistic bodies; and it explores the implications of living as linguistic bodies in perpetual becoming, applying the concept of linguistic bodies to questions of language acquisition, parenting, autism, grammar, symbol, narrative, and gesture, and to such ethical concerns as microaggression, institutional speech, and pedagogy. (shrink)

This book presents the framework for a new, comprehensive approach to cognitive science. The proposed paradigm, enaction, offers an alternative to cognitive science's classical, first-generation Computational Theory of Mind. _Enaction_, first articulated by Varela, Thompson, and Rosch in _The Embodied Mind_, breaks from CTM's formalisms of information processing and symbolic representations to view cognition as grounded in the sensorimotor dynamics of the interactions between a living organism and its environment. A living organism enacts the world it lives in; its embodied (...) action in the world constitutes its perception and thereby grounds its cognition. _Enaction_ offers a range of perspectives on this exciting new approach to embodied cognitive science. Some chapters offer manifestos for the enaction paradigm; others address specific areas of research, including artificial intelligence, developmental psychology, neuroscience, language, phenomenology, and culture and cognition. Three themes emerge as testimony to the originality and specificity of enaction as a paradigm: the relation between first-person lived experience and third-person natural science; the ambition to provide an encompassing framework applicable at levels from the cell to society; and the difficulties of reflexivity. Taken together, the chapters offer nothing less than the framework for a far-reaching renewal of cognitive science. Contributors: Renaud Barbaras, Didier Bottineau, Giovanna Colombetti, Diego Cosmelli, Hanne De Jaegher, Ezequiel A. Di Paolo. Andreas K. Engel, Olivier Gapenne, Véronique Havelange, Edwin Hutchins, Michel Le Van Quyen, Rafael E. Núñez, Marieke Rohde, Benny Shanon, Maxine Sheets-Johnstone, Adam Sheya, Linda B. Smith, John Stewart, Evan Thompson. (shrink)

Negation can be considered a shared social action that develops since early infancy with very basic acts of refusals or rejection. Inspired by an approach to the embodiment of concepts known as Multiple Representation Theories, the present paper explores negation as an embodied action that relies on both sensorimotor and linguistic/social information. Despite the different variants, MRT accounts share the basic ideas that both linguistic/social and sensorimotor information concur to the processes of concepts formation and representation and that (...) the balance between these components depends on the kind of concept, the context, or the performed task. In the present research we will apply the MRT framework for exploring negation in Italian sign language. The nature of negation in LIS has been explored in continuity with the co-speech gesture where negative elements are encoded through differentiated prosodic and gestural strategies across languages. Data have been collected in naturalistic settings that may allow a much wider understanding of negation both in speech and in spoken language with a semi-structured interview. Five LIS participants with age range 30–80 were recruited and interviewed with the aim of understanding the continuity between gesture and sign in negation. Results highlight that negation utterances mirror the functions of rejection, non-existence and denial that have been described in language acquisition both in deaf and hearing children. These different steps of acquisition of negation show a different balance between sensorimotor, linguistic and social information in the construction of negative meaning that the MRT is able to enlighten. (shrink)

As Macnamara (1978) once asked, how can we talk about what we see? We report on a study manipulating realistic dynamic scenes and sentences aiming to understand the interaction between linguistic and visual representations in real-world situations. Specifically, we monitored participants’ eye movements as they watched video clips of everyday scenes while listening to sentences describing these scenes. We manipulated two main variables. The first was the semantic class of the verb in the sentence and the second was the action/motion (...) of the agent in the unfolding event. The sentences employed two verb classes—causatives (e.g., break) and perception/psychological (e.g., notice)—which impose different constraints on the nouns that serve as their grammatical complements. The scenes depicted events in which agents either moved towards a target object (always the referent of the verb-complement noun), away from it, or remained neutral performing a given activity (such as cooking). Scenes and sentences were synchronized such that the verb onset corresponded to the first video frame of the agent motion towards or away from the object. Results show effects of agent motion but weak verb-semantic restrictions: causatives draw more attention to potential referents of their grammatical complements than perception verbs only when the agent moves towards the target object. Crucially, we found no anticipatory verb-driven eye movements toward the target object, contrary to studies using non-naturalistic and static scenes. We propose a model in which linguistic and visual computations in real-world situations occur largely independent of each other during the early moments of perceptual input, but rapidly interact at a central, conceptual system using a common, propositional code. Implications for language use in real world contexts are discussed. (shrink)

Advances in neuroscience implicate reentrant signaling as the predominant form of communication between brain areas. This principle was used in a series of masking experiments that defy explanation by feed-forward theories. The masking occurs when a brief display of target plus mask is continued with the mask alone. Two masking processes were found: an early process affected by physical factors such as adapting luminance and a later process affected by attentional factors such as set size. This later process is called (...) masking by object substitution, because it occurs whenever there is a mismatch between the reentrant visual representation and the ongoing lower level activity. Iterative reentrant processing was formalized in a computational model that provides an excellent fit to the data. The model provides a more comprehensive account of all forms of visual masking than do the long-held feed-forward views based on inhibitory contour interactions. (shrink)

Movement perception and its role in aesthetic experience have been often studied, within empirical aesthetics, in relation to the human body. No such specificity has been defined in neuroimaging studies with respect to contents lacking a human form. The aim of this work was to explore, through functional magnetic imaging (fMRI), how perceived movement is processed during the aesthetic judgment of paintings using two types of content: human subjects and scenes of nature. Participants, untutored in the arts, were shown the (...) stimuli and asked to make aesthetic judgments. Additionally, they were instructed to observe the paintings and to rate their perceived movement in separate blocks. Observation highlighted spontaneous processes associated with aesthetic experience, whereas movement judgment outlined activations specifically related to movement processing. The ratings recorded during aesthetic judgment revealed that nature scenes received higher scored than human content paintings. The imaging data showed similar activation, relative to baseline, for all stimuli in the three tasks, including activation of occipito-temporal areas, posterior parietal and premotor cortices. Contrast analyses within aesthetic judgment task showed that human content activated, relative to nature, precuneus, fusiform gyrus and posterior temporal areas, whose activation was prominent for dynamic human paintings. In contrast, nature scenes activated, relative to human stimuli, occipital and posterior parietal cortex/precuneus, involved in visuospatial exploration and pragmatic coding of movement, as well as central insula. Static nature paintings further activated, relative to dynamic nature stimuli, central and posterior insula. Besides insular activation, which was specific for aesthetic judgment, we found a large overlap in the activation pattern characterizing each stimulus dimension (content and dynamism) across observation, aesthetic judgment and movement judgment tasks. These findings support the idea that the aesthetic evaluation of artworks depicting both human subjects and nature scenes involves a motor component, and that the associated neural processes occur quite spontaneously in the viewer. Furthermore, considering the functional roles of posterior and central insula, we suggest that nature paintings may evoke aesthetic processes requiring an additional proprioceptive and sensori-motor component implemented by “motor accessibility” to the represented scenario, which is needed to judge the aesthetic value of the observed painting. (shrink)

The literature on algorithmic fairness has examined exogenous sources of biases such as shortcomings in the data and structural injustices in society. It has also examined internal sources of bias as evidenced by a number of impossibility theorems showing that no algorithm can concurrently satisfy multiple criteria of fairness. This paper contributes to the literature stemming from the impossibility theorems by examining how informational richness affects the accuracy and fairness of predictive algorithms. With the aid of a computer simulation, we (...) show that informational richness is the engine that drives improvements in the performance of a predictive algorithm, in terms of both accuracy and fairness. The centrality of informational richness suggests that classification parity, a popular criterion of algorithmic fairness, should be given relatively little weight. But we caution that the centrality of informational richness should be taken with a grain of salt in light of practical limitations, in particular, the so-called bias-variance trade off. (shrink)

Studying trust in the context of human-robot interaction is of great importance given the increasing relevance and presence of robotic agents in the social sphere, including educational and clinical. We investigated the acquisition, loss and restoration of trust when preschool and school-age children played with either a human or a humanoid robot in-vivo. The relationship between trust and the representation of the quality of attachment relationships, Theory of Mind, and executive function skills was also investigated. Additionally, to outline children’s (...) beliefs about the mental competencies of the robot, we further evaluated the attribution of mental states to the interactive agent. In general, no substantial differences were found in children’s trust in the play-partner as a function of agency (human or robot). Nevertheless, 3-years-olds showed a trend toward trusting the human more than the robot, as opposed to 7-years-olds, who displayed the reverse pattern. These findings align with results showing that, for 3 and 7-year-olds, the cognitive ability to switch was significantly associated with trust restoration in the human and the robot, respectively. Additionally, supporting previous findings, we found a dichotomy between attributions of mental states to the human and robot and children’s behavior: while attributing to the robot significantly lower mental states than the human, in the trusting game children behaved in a similar way when they related to the human and the robot. Altogether, the results of this study highlight that similar psychological mechanisms are at play when children are to establish a novel trustful relationship with a human and robot partner. Furthermore, the findings shed light on the interplay – during development – between children’s quality of attachment relationships and the development of a Theory of Mind, which act differently on trust dynamics as a function of the children’s age as well as the interactive partner’s nature (human vs. robot). (shrink)

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where (...) α * = λ = ω. (shrink)

In this book we offer a theory of the self, whose core ideas are that the self is a process of self-representing, and this process aims mainly at defending the self-conscious subject against the threat of its metaphysical inconsistence. In other words, the self is essentially a repertoire of psychological manoeuvres whose outcome is a self-representation aimed at coping with the fundamental fragility of the human subject. Our picture of the self differs from both the idealist and the eliminative (...) approaches widely represented in contemporary discussion. Against the idealist approach, we deny that the self is something primitive and logically prior. Rather, we take it to be the result of a process of construction that starts with subpersonal unconscious processes. On the other hand, we also reject the anti-realistic, eliminative argument that, from the non-primary, derivative nature of the self, infers its status as an illusory by-product of real neurobiological events, devoid of any explanatory role. (shrink)