Influential theories on moral judgments propose that they rely either on emotions or on innate moral principles. In contrast, the mental model theory postulates that moral judgments rely on reasoning, either intuition or deliberation. The theory allows for the possibility that intuitions lead to utilitarian judgments. This paper reports two experiments involving fifth-grade children, adolescents, and adults; the results revealed that children reason intuitively to resolve moral dilemmas in which action and inaction lead to different outcomes. In particular, the results (...) showed female children to be more utilitarian than female adults in resolving classical moral dilemmas: they preferred an action that achieved a good outcome for a greater number of people. Within the mental model theory’s framework there is no reason to expect that females and males differ in their ability to reason, but at the moment the results for females cannot be generalized to males who were not properly represented in the adults groups of the two experiments. The result revealing that (female) children are more utilitarian than (female) adults, which is hard to explain via many current theories, was predicted by the mental model theory. (shrink)

We continue the investigation, initiated in Salibra et al. (Found Sci, 2020), of Boolean-like algebras of dimension n (nBA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\textrm{BA}$$\end{document}s), algebras having n constants e1,⋯,en\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf e_1,\dots,\mathsf e_n$$\end{document}, and an (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document}-ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of nBA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\textrm{BA}$$\end{document}s share many remarkable properties with the variety of Boolean algebras and with primal varieties. Putting to good use the concept of a central element, we extend the Boolean power construction to that of a semiring power and we prove two representation theorems: (i) Any pure nBA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\textrm{BA}$$\end{document} is isomorphic to the algebra of n-central elements of a Boolean vector space; (ii) Any member of a variety of nBAs with one generator is isomorphic to a Boolean power of this generator. This yields a new proof of Foster’s theorem on primal varieties. (shrink)

We introduce Boolean-like algebras of dimension n ($$n{\mathrm {BA}}$$ n BA s) having n constants $${{{\mathsf {e}}}}_1,\ldots,{{{\mathsf {e}}}}_n$$ e 1, …, e n, and an $$(n+1)$$ ( n + 1 ) -ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of $$n{\mathrm {BA}}$$ n BA s share many remarkable properties with the variety of Boolean algebras and with primal varieties. The $$n{\mathrm {BA}}$$ n BA s provide the (...) algebraic framework for generalising the classical propositional calculus to the case of n–perfectly symmetric–truth-values. Every finite-valued tabular logic can be embedded into such a n-valued propositional logic, $$n{\mathrm {CL}}$$ n CL, and this embedding preserves validity. We define a confluent and terminating first-order rewriting system for deciding validity in $$n{\mathrm {CL}}$$ n CL, and, via the embeddings, in all the finite tabular logics. (shrink)

The deep comprehension of a text is tantamount to the construction of an articulated mental model of that text. The number of correct recollections is an index of a learner's mental model of a text. We assume that another index of comprehension is the timing of the gestures produced during text recall; gestures are simultaneous with speech when the learner has built an articulated mental model of the text, whereas they anticipate the speech when the learner has built a less (...) articulated mental model. The results of four experiments confirm the predictions deriving from our assumptions for both children and adults. Provided that the recollections are correct, the timing of gestures can differ and can be considered a further measure of the quality of the mental model, beyond the number of correct recollections. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

Henrich et al. address how culture leads to cognitive variability and recommend that researchers be critical about the samples they investigate. However, there are other sources of variability, such as individual strategies in reasoning and the content and context on which processes operate. Because strategy and content drive variability, those factors are of primary interest, while culture is merely incidental.

Henrich et al. address how culture leads to cognitive variability and recommend that researchers be critical about the samples they investigate. However, there are other sources of variability, such as individual strategies in reasoning and the content and context on which processes operate. Because strategy and content drive variability, those factors are of primary interest, while culture is merely incidental.

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used (...) a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re‐evaluates current theories of syllogistic reasoning in the light of these results. (shrink)

In Engineering Philosophy, the author explores how the concerns of philosophers are relevant to engineering thought and practice in negotiating tradeoffs in diagnosing failure, in constructing adequate models and simulations, and in teaching.

We extend to the exponential connectives of linear logic the study initiated in Bucciarelli and Ehrhard 247). We define an indexed version of propositional linear logic and provide a sequent calculus for this system. To a formula A of indexed linear logic, we associate an underlying formula of linear logic, and a family A of elements of , the interpretation of in the category of sets and relations. Then A is provable in indexed linear logic iff the family A (...) is contained in the interpretation of some proof of . We extend to this setting the product phase semantics of indexed multiplicative additive linear logic introduced in Bucciarelli and Ehrhard , defining the symmetric product phase spaces. We prove a soundness result for this truth-value semantics and show how a denotational model of linear logic can be associated to any symmetric product phase space. Considering a particular symmetric product phase space, we obtain a new coherence space model of linear logic, which is non-uniform in the sense that the interpretation of a proof of !A−B contains informations about the behavior of this proof when applied to “chimeric” arguments of type A . In this coherence semantics, an element of a web can be strictly coherent with itself, or two distinct elements can be “neutral”. (shrink)

We study the notion of logical relation in the coherence space semantics of multiplicative-additive linear logic . We show that, when the ground-type logical relation is “closed under restrictions”, the logical relation associated to any type can be seen as a map associating facts of a phase space to families of points of the web of the corresponding coherence space. We introduce a sequent calculus extension of whose formulae denote these families of points. This logic admits a truth-value semantics in (...) the previously mentioned phase space, and this truth-value semantics faithfully describes the logical relation model we started from. Then we generalize this notion of phase space, we prove a truth-value completeness result for and we derive from any phase model of a denotational model for . Using the truth-value completeness result, we obtain a weak denotational completeness result based on this new denotational semantics. (shrink)

In this paper, I present a framework where possible relations between learning and mental models are explored. In particular, I’ll be concerned with non-symbolic gestures accompanying discourse and their role in inducing the construction of models and therefore deep comprehension and learning in the listener. Also, I’ll be concerned with cognitive and socio-cognitive conflicts and their roles in inducing construction of alternative models of a problem and therefore in learning to reason. Human ability to learn is of great importance for (...) individuals interested in change. Indeed, to learn both declarative and procedural knowledge means to change, and in order to be able to intervene on change in a desired way it is necessary to have a theory of the mental representations and processes involved in learning and a theory of the communication and contexts that favour learning. (shrink)

Following the assumptions of the mental model theory and its account of moral judgements, we argue for a main role of reasoning in moral judgements, especially in dealing with moral conflicts. In four experiments, we invited adult participants to evaluate scenarios describing moral or immoral actions. Our results confirm the predictions deriving from our assumptions: Given a moral or immoral scenario, the manipulation of the propositions which refer to norms and values results in a scenario eliciting a moral conflict ; (...) when invited to create conflict versions from no-conflict versions of moral or immoral scenarios, individuals manipulate the propositions in the scenario which describe norms and values rather than emotional factors ; the evaluation of conflict scenarios takes longer than the evaluation of no-conflict scenarios, and this is because conflict scenarios involve more deliberative reasoning. We discuss our results in relation to competing.. (shrink)

In recent research, some of the present authors introduced the concept of an $n$-dimensional Boolean algebra and its corresponding propositional logic $n\textrm{CL}$, generalizing the Boolean propositional calculus to $n\geq 2$ perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for $n\textrm{CL}$, named $n\textrm{LK}$. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that $n\textrm{LK}$ enjoys the cut admissibility property. The latter relies on the generalization to the $n$-ary case (...) of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters. (shrink)

The texts (and talk) of engineers take different forms. In this essay, I present and critique several texts written for different purposes and audiences but all intended to convey to the reader the technical details of whatever they are about—whether a textbook passage describing the fundamental behavior of an electrical component, a journal article about a mathematical technique intended for use in design optimization, a memo to co-workers within a firm about a heat transfer analysis of a remotely sited building, (...) or a general introduction to the field of? ergonomics? My aim is to explore how the ways in which engineers describe and document their problems and projects frame what they accept, display and profess as useful knowledge. In this I am particularly interested in how engineers envision the ‘users’ of, or participants in, their productions. Like science, engineering texts are written as if they were timeless and untainted by socio-cultural features. However, a technical treatise is not devoid of metaphor or creative rendering of events; there is always a narrative within which worldly data and instrumental logic is embedded—but it is a story in which the passive voice prevails, history is irrelevant, and the human actor or agent is painted in quantitative parameters fitting the occasion. Whether this rhetoric can be sustained in the face of challenges to traditional ways of doing engineering is an open question. (shrink)

Stanovich & West interpret errors in syllogistic reasoning in terms of computational limitations. I argue that the variety of strategies used by reasoners in solving syllogisms requires us to consider also performance errors. Although reasoners' performance from one trial to another is quite consistent, it can be different, in line with the definition of performance errors. My argument has methodological implications for reasoning theories.

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal (...) foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

We consider a notion of sequential functional of finite type, more generous than the familiar notion embodied in Plotkin's language PCF. We study both the “full” and “effective” partial type structures arising from this notion of sequentiality. The full type structure coincides with that given by the strongly stable model of Bucciarelli and Ehrhard; it has also been characterized by van Oosten in terms of realizability over a certain combinatory algebra. We survey and relate several known characterizations of these (...) type structures, and obtain some new ones. We show that every finite type can be obtained as a retract of the pure type , and hence that all elements of the effective type structure are definable in PCF extended by a certain universal functional H. We also consider the relationship between our notion of sequentially computable functional and other known notions of higher-type computability. (shrink)

The mental model theory claims that the ability to falsify is at the core of human rationality. We assume that cognitive conflicts (CCs) and socio-cognitive conflicts (SCCs) induce falsification, and thus improve syllogistic reasoning performance. Our first study assesses adults’ ability to reason in two different conditions in a single experimental session. In both conditions the participants are presented with conclusions alternative to their own. In the CC condition they are told that these conclusions are casual, in the SCC condition (...) they are told they have been produced by another individual. The second study is analogous to the first, with the exception that the participants deal with the two conditions in two different experimental sessions. The overall results reveal that falsification is enhanced by conflicts experienced at the cognitive level. The results also reveal that learning to reason occurs in adults, when tested in two distinct experimental periods. (shrink)

This study concerned the role of gestures that accompany discourse in deep learning processes. We assumed that co‐speech gestures favor the construction of a complete mental representation of the discourse content, and we tested the predictions that a discourse accompanied by gestures, as compared with a discourse not accompanied by gestures, should result in better recollection of conceptual information, a greater number of discourse‐based inferences drawn from the information explicitly stated in the discourse, and poorer recognition of verbatim of the (...) discourse. The results of three experiments confirmed these predictions. (shrink)

In this paper we deal with two types of reasoning: induction, and deduction First, we present a unified computational model of deductive reasoning through models, where deduction occurs in five phases: Construction, Integration, Conclusion, Falsification, and Response. Second, we make an attempt, to analyze induction through the same phases. Our aim is an explorative evaluation of the mental processes possibly shared by deductive and inductive reasoning.

We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the “extensional projections” of some sequential algorithms. We define a model of PCF where morphisms are “extensional” sequential algorithms and prove that any equation between PCF terms which holds (...) in this model also holds in the strongly stable model. (shrink)

This article aims to develop new conceptions of the psychosocial dynamics that drive the re-romanticization of domestic femininity in current financialized capitalism. Feminist scholars have described this heightened cultivation of mothering as a reparative move in response to irreconcilable tensions between cultural ideals of the ‘balancing mother’ and ‘lean-in femininity’. This article adds a materialist-psychosocial lens to these conceptions, to enhance understanding of what drives this craving for domestic femininity. Drawing on a free-association narrative interview study with couples in the (...) financial elite in the comparatively gender-egalitarian Norwegian context, I describe a specific emotional mechanism that resists democratization of gender in this specific group. The interviews reveal a felt need to cultivate ‘the human side of things’ at safe distance from the competitiveness of ‘hard-core finance’. The Nordic earner–carer model with its entwinement of care and professional pursuits, cultivated by the more self-fulfilment-oriented parts of the professional middle-class appears not only unwanted but threatening. In my analysis, I retrieve and develop a psychoanalytically inspired historical-materialist feminism, one that perceives of the gendered division of work as a split in modes of focusing human energy. I suggest that the resurgent cultivation of domestic femininity is nurtured by a self-energizing antagonism between competitive and relational practices. I further argue that the cultivation of domestic femininity in these financial couples points to a potential antagonism between the democratization of love and the specific anxiety-driven competitiveness to which this financial-elite group may be particularly susceptible. (shrink)

This chapter contains section titled: Introductory Remarks The Cartesian Background Impressions and Ideas Passions as Reflective Impressions Direct and Indirect Passions Association and the Individuation of Passions Perception and Perceiving Passions and Moral Sentiments Notes References Further reading.