469 research outputs found

    Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

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    We examined matching bias in syllogistic reasoning by analysing response times, confidence ratings, and individual differences. Roberts’ (2005) “negations paradigm” was used to generate conflict between the surface features of problems and the logical status of conclusions. The experiment replicated matching bias effects in conclusion evaluation (Stupple & Waterhouse, 2009), revealing increased processing times for matching/logic “conflict problems”. Results paralleled chronometric evidence from the belief bias paradigm indicating that logic/belief conflict problems take longer to process than non-conflict problems (Stupple, Ball, Evans, & Kamal-Smith, 2011). Individuals’ response times for conflict problems also showed patterns of association with the degree of overall normative responding. Acceptance rates, response times, metacognitive confidence judgements, and individual differences all converged in supporting dual-process theory. This is noteworthy because dual-process predictions about heuristic/analytic conflict in syllogistic reasoning generalised from the belief bias paradigm to a situation where matching features of conclusions, rather than beliefs, were set in opposition to logic

    False Persuasion, Superficial Heuristics, and the Power of Logical Form to Test the Integrity of Legal Argument

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    This Article will generally describe philosophical logic, logical form, and logical fallacy. Further, it will explain one specific logical fallacy—the Fallacy of Negative Premises—as well as how courts have used the Fallacy of Negative Premises to evaluate legal arguments. Last, it will explain how lawyers, judges, and law students can use the Fallacy of Negative Premises to make and evaluate legal argument

    Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors

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    Boundary algebra [BA] is a simpler notation for Spencer-Brown’s (1969) primary algebra [pa], the Boolean algebra 2, and the truth functors. The primary arithmetic [PA] consists of the atoms ‘()’ and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting the presence or absence of () into a PA formula yields a BA formula. The BA axioms are "()()=()" (A1), and "(()) [=?] may be written or erased at will” (A2). Repeated application of these axioms to a PA formula yields a member of B= {(),?} called its simplification. (a) has two intended interpretations: (a) ? a? (Boolean algebra 2), and (a) ? ~a (sentential logic). BA is self-dual: () ? 1 [dually 0] so that B is the carrier for 2, ab ? a?b [a?b], and (a)b [(a(b))] ? a=b, so that ?=() [()=?] follows trivially and B is a poset. The BA basis abc= bca (Dilworth 1938), a(ab)= a(b), and a()=() (Bricken 2002) facilitates clausal reasoning and proof by calculation. BA also simplifies normal forms and Quine’s (1982) truth value analysis. () ? true [false] yields boundary logic.G. Spencer Brown; boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; C.S. Peirce; existential graphs.

    Boundary Algebra: A Simpler Approach to Boolean Algebra and the Sentential Connectives

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    Boundary algebra [BA] is a algebra of type , and a simplified notation for Spencer-Brown’s (1969) primary algebra. The syntax of the primary arithmetic [PA] consists of two atoms, () and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting, indifferently, the presence or absence of () into a PA formula yields a BA formula. The BA axioms are A1: ()()= (), and A2: “(()) [abbreviated ‘⊥’] may be written or erased at will,” implying (⊥)=(). The repeated application of A1 and A2 simplifies any PA formula to either () or ⊥. The basis for BA is B1: abc=bca (concatenation commutes & associates); B2, ⊥a=a (BA has a lower bound, ⊥); B3, (a)a=() (BA is a complemented lattice); and B4, (ba)a=(b)a (implies that BA is a distributive lattice). BA has two intended models: (1) the Boolean algebra 2 with base set B={(),⊥}, such that () ⇔ 1 [dually 0], (a) ⇔ a′, and ab ⇔ a∪b [a∩b]; and (2) sentential logic, such that () ⇔ true [false], (a) ⇔ ~a, and ab ⇔ a∨b [a∧b]. BA is a self-dual notation, facilitates a calculational style of proof, and simplifies clausal reasoning and Quine’s truth value analysis. BA resembles C.S. Peirce’s graphical logic, the symbolic logics of Leibniz and W.E. Johnson, the 2 notation of Byrne (1946), and the Boolean term schemata of Quine (1982).Boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; G. Spencer-Brown; C.S. Peirce; existential graphs

    Executive functions and pilot characteristics predict flight simulator performance in general aviation pilots

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    In general aviation, 85% of the crashes seem to be caused by pilots' errors (Li, Baker, Grabowski, & Rebok, 2001) and 46% of the crashes occur at airports (Li & Baker, 1999). It is important to determine if the same factors influence the flying performance and the landing decision making and to uncover which factors, among the pilot's cognitive status, personality traits, and experience, are the most predictive. We examined in 24 general aviation pilots the relationship between those factors and the flying performance and weather-related decision-making relevance. The cognitive assessment encompassed the three basic executive functions (Miyake et al., 2000), reasoning, and psychomotor velocity. The personal characteristics were age, flight experience, and level of impulsivity. Reasoning, updating in working memory, and flight experience were predictive of the flight performance. In addition, updating in working memory, flight experience, and level of impulsivity were linked with weather-related decision-making relevance

    The Algebra of Logic Tradition

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    The algebra of logic, as an explicit algebraic system showing the underlying mathematical structure of logic, was introduced by George Boole (1815-1864) in his book The Mathematical Analysis of Logic (1847). The methodology initiated by Boole was successfully continued in the 19th century in the work of William Stanley Jevons (1835-1882), Charles Sanders Peirce (1839-1914), Ernst Schröder (1841-1902), among many others, thereby establishing a tradition in (mathematical) logic. From Boole's first book until the influence after WWI of the monumental work Principia Mathematica (1910 1913) by Alfred North Whitehead (1861-1947) and Bertrand Russell (1872-1970), versions of thealgebra of logic were the most developed form of mathematical above allthrough Schröder's three volumes Vorlesungen über die Algebra der Logik(1890-1905). Furthermore, this tradition motivated the investigations of Leopold Löwenheim (1878-1957) that eventually gave rise to model theory. Inaddition, in 1941, Alfred Tarski (1901-1983) in his paper On the calculus of relations returned to Peirce's relation algebra as presented in Schröder's Algebra der Logik. The tradition of the algebra of logic played a key role in thenotion of Logic as Calculus as opposed to the notion of Logic as Universal Language . Beyond Tarski's algebra of relations, the influence of the algebraic tradition in logic can be found in other mathematical theories, such as category theory. However this influence lies outside the scope of this entry, which is divided into 10 sections.Fil: Burris, Stanley. University of Waterloo; CanadáFil: Legris, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Interdisciplinario de Economía Politica de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Instituto Interdisciplinario de Economía Politica de Buenos Aires; Argentin

    Individual differences and strategies for human reasoning

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    Theories of human reasoning have tended to assume cognitive universality, i. e. that all individuals reason in basically the same way. However, some research (e. g. that of Ford. 1995) has found evidence of individual differences in the strategies people use for syllogistic reasoning. This thesis presents a series of experiments which aimed to identify individual differences in strategies for human reasoning and investigate their nature and aetiology. Experiment 1 successfully replicated and extended Ford (1995) and provided further evidence that most individuals prefer to reason with either verbal-propositional or visuo-spatial representations. Data from verbal and written protocols showed that verbal reasoners tended to use a method of substitution whereby they obtain a value for the common term from one premise and then simply substitute it in the other premise to obtain a conclusion. Spatial reasoners, on the other hand, presented protocols which resembled Euler circles and described the syllogistic premises in terms of sets and subsets. Experiment 2 provided some further qualitative evidence about the nature of such strategies, especially the verbal reasoners, showing that within strategy variations occurred. Experiment 3 extended this line of research, identifying a strong association between verbal and spatial strategies for syllogistic reasoning and abstract and concrete strategies for transitive inference (the latter having originally been identified by Egan and Grimes- Farrow, 1982). Experiments 1-3 also showed that inter-strategic differences in accuracy are generally not observed, hence, reasoners present an outward appearance of ubiquity despite underlying differences in reasoning processes. Experiments 5 and 6 investigated individual differences in cognitive factors which may underpin strategy preference. Whilst no apparent effects of verbal and spatial ability or cognitive style were found, reasoners did appear to draw differentially on the verbal and spatial components of working memory. Confirmatory factor analysis showed that whilst verbal reasoners draw primarily on the verbal memory resource, spatial reasoners draw both on this and on spatial resource. Overall, these findings have important implications for theories of human reasoning, which need to take into account possible individual differences in strategies if they are to present a truly comprehensive account of how people reason.Economic and Social Research Counci

    Many Labs 2 : Investigating Variation in Replicability Across Sample and Setting

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    We conducted preregistered replications of 28 classic and contemporary published findings with protocols that were peer reviewed in advance to examine variation in effect magnitudes across sample and setting. Each protocol was administered to approximately half of 125 samples and 15,305 total participants from 36 countries and territories. Using conventional statistical significance (p &lt; .05), fifteen (54%) of the replications provided evidence in the same direction and statistically significant as the original finding. With a strict significance criterion (p &lt; .0001), fourteen (50%) provide such evidence reflecting the extremely high powered design. Seven (25%) of the replications had effect sizes larger than the original finding and 21 (75%) had effect sizes smaller than the original finding. The median comparable Cohen’s d effect sizes for original findings was 0.60 and for replications was 0.15. Sixteen replications (57%) had small effect sizes (&lt; .20) and 9 (32%) were in the opposite direction from the original finding. Across settings, 11 (39%) showed significant heterogeneity using the Q statistic and most of those were among the findings eliciting the largest overall effect sizes; only one effect that was near zero in the aggregate showed significant heterogeneity. Only one effect showed a Tau &gt; 0.20 indicating moderate heterogeneity. Nine others had a Tau near or slightly above 0.10 indicating slight heterogeneity. In moderation tests, very little heterogeneity was attributable to task order, administration in lab versus online, and exploratory WEIRD versus less WEIRD culture comparisons. Cumulatively, variability in observed effect sizes was more attributable to the effect being studied than the sample or setting in which it was studied. Data, materials and code available at: https://osf.io/8cd4r/</a

    Fuzzy Natural Logic in IFSA-EUSFLAT 2021

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    The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications

    Necessity, Possibility and the Search for Counterexamples in Human Reasoning

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    Abstract Necessity, Possibility and the Search for Counterexamples in Human Reasoning Sylvia Mary Parnell Serpell This thesis presents a series of experiments where endorsement rates, latencies and measures of cognitive ability were collected, to investigate the extent to which people search for counterexamples under necessity instructions, and alternative models under possibility instructions. The research was motivated by a syllogistic reasoning study carried out by Evans, Handley, Harper, and Johnson-Laird (1999), and predictions were derived from mental model theory (Johnson-Laird, 1983; Johnson-Laird & Byrne, 1991). With regard to the endorsement rate data: Experiment 1 failed to find evidence that a search for counterexamples or alternative models took place. In contrast experiment 2 (transitive inference) found some evidence to support the search for alternative models under possibility instructions, and following an improved training session, experiment 3 produced strong evidence to suggest that people searched for other models; which was mediated by cognitive ability. There was also strong evidence from experiments 4, 5 and 6 (abstract and everyday conditionals) to support the search for counterexamples and alternative models. Furthermore it was also found that people were more likely to find alternative causes when there were many that could be retrieved from their everyday knowledge, and that people carried out a search for counterexamples with many alternative causes under necessity instructions, and across few and many causal groups under possibility instructions. .The evidence from the latency data was limited and inconsistent, although people with higher cognitive ability were generally quicker in completing the tasks
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