A survey of deduction theorems for the propositional calculi

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A survey of deduction theorems for the propositional calculi

     

A schema of deduction theorems for the propositional calculus

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A schema of deduction theorems for the propositional calculus

     

The semantics of 'unless' conditionals: evidence from 'unless' and disjunctive inferences

We report the results of an experiment investigating conditional inferences from conditional assertions such as 'Juan won't go to León unless Nuria goes to Madrid' and 'Either Nuria goes to Madrid or Juan won't go to León'. This experiment addresses Dancygier's claims about the semantics of 'unless' by examining inferential endorsements of 'not-A unless B' and 'Either B or not-A' in the canonical order, presenting the categorical premise after the conditional assertions, and in the inverse order, presenting the categorical premise before the conditional assertions. The results of the experiment confirm that the representation of 'unless' includes two possibilities, although as Dancygier holds one of the possibilities may not be complete. The implications of the results are discussed in the context of the strategic nature of conditional reasoning and recent convergent theories of linguistic processing.     

The psychology of inferring conditionals from disjunctions: A probabilistic study

There is a new probabilistic paradigm in the psychology of reasoning that is, in part, based on results showing that people judge the probability of the natural language conditional, if $A$then $B$, $P\left(ifAthenB\right)$, to be the conditional probability, $P(B\mid A)$. We apply this new approach to the study of a very common inference form in ordinary reasoning: inferring the conditional if not-$A$then $B$ from the disjunction $A$ or $B$. We show how this inference can be strong, with $P$(if not-$A$then $B$) “close to” $P\left(AorB\right)$, when $A$ or $B$ is non-constructively justified. When $A$ or $B$ is constructively justified, the inference can be very weak. We also define suitable measures of “closeness” and “constructivity”, by providing a probabilistic analysis of these notions.     

A deduction theorem schema for deductive systems of propositional logics

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) _s q.     

Consequential conditionals: invited and suppressed inferences from valued outcomes

Consequential conditionals are defined as "if P then Q" statements, where P is an action, and Q a predicted outcome of this action, which is either desirable or undesirable to the agent. Experiment 1 shows that desirable (viz. undesirable) outcomes invite an inference to the truth (viz. falsity) of their antecedent. Experiment 2 shows that the more extreme the outcome is, the stronger the invited inference is. Experiment 3 shows that modus ponens from premises "If A then C, A" can be suppressed with the introduction of a consequential conditional, "If C then Q," where Q is an undesirable outcome. Experiment 4 shows that the more undesirable Q is, the larger the suppression is. The authors discuss how these results can enrich current approaches of conditional inference on the basis of mental models, complementary necessary conditions, and conditional probabilities.     

The negations of conjunctions,conditionals, and disjunctions

How do reasoners understand and formulate denials of compound assertions, such as conjunctions and disjunctions? A theory based on mental models postulates that individuals enumerate models of the various possibilities consistent with the assertions. It therefore predicts a novel interaction: in affirmations, conjunctions, A and B, which refer to one possibility, should be easier to understand than disjunctions, A or B, which refer to more than one possibility; in denials, conjunctions, not(A and B), which refer to more than one possibility, should be harder to understand than disjunctions, not(A or B), which do not. Conditionals are ambiguous and they should be of intermediate difficulty. Experiment 1 corroborated this trend with a task in which the participants selected which possibilities were consistent with assertions, such as: Bob denied that he wore a yellow shirt and he wore blue pants on Tuesday. Experiment 2 likewise showed that participants' own formulations of verbal denials yielded the same trend in which denials of conjunctions were harder than denials of conditionals, which in turn were harder than denials of disjunctions.     

Sex-role acquisition,parental behavior,and sexual orientation: Some tentative hypotheses

It was hypothesized that sexual orientation is not an aspect of sex-role socialization, but is acquired during a sensitive period from birth to 3 years through physical contact with adults. This is tentatively supported by evidence suggesting that (a) sexual orientation is highly resistant to change after adolescence; (b) infants respond to sexual stimulation and discriminate between the sexes; (c) gender identity is fixed between birth and 3 years of age; (d) during their infancy, homosexuals were psychosocially and presumably physically responded to as children of the opposite sex; (e) parents touch boys and girls differently. Stronger support for the hypothesis must be gained from longitudinal observation of parent-infant physical and social interaction and the infant's eventual sexual orientation.     

Some comments on the projectibility of anthropological hypotheses: Samoa briefly revisited

The purpose of this article is to examine the applicability of the theory of projection for Anthropological hypotheses. The claim is made that Goodman's classic statement of the problem does not apply in its entirety to actual Anthropological hypotheses. The recent Freeman-Mead debate is employed as a framework for the discussion, illustrating that the issue of projectibility, while central for the social sciences, is best used as a backdrop to illustrate several important methodological problems. For Anthropology, and other related social sciences, the central methodological problem, which is directly related to the projectibility one, is the development and justification of evidence-rules that can be used for a theory of confirmation. A preliminary attempt is then made to articulate the nature of these rules within the general Hempelian framework of qualitative confirmation.     

Parsing as deduction: The use of knowledge of language

Hypothesising that the human parser is a specialized deductive device in which Universal Grammar and parameter settings are represented as axioms provides a model of how knowledge of language can be put to use. The approach is explained via a series of model deductive parsers for Government and Binding Theory, all of which use the same knowledge of language (i.e., underlying axiom system) but differ as to how they put this knowledge to use (i.e., they use different inference control strategies). They differ from most other GB parsers in that the axiom system directly reflects the modular structure of GB theory and makes full use of the multiple levels of reprepresentation posited in GB theory.     

Illusory inferences from a disjunction of conditionals: a new mental models account

(Johnson-Laird, P.N., & Savary, F. (1999, Illusory inferences: a novel class of erroneous deductions. Cognition, 71, 191-229.) have recently presented a mental models account, based on the so-called principle of truth, for the occurrence of inferences that are compelling but invalid. This article presents an alternative account of the illusory inferences resulting from a disjunction of conditionals. In accordance with our modified theory of mental models of the conditional, we show that the way individuals represent conditionals leads them to misinterpret the locus of the disjunction and prevents them from drawing conclusions from a false conditional, thus accounting for the compelling character of the illusory inference.     

Age and motives for volunteering: testing hypotheses derived from socioemotional selectivity theory

Following a meta-analysis of the relations between age and volunteer motives (career, understanding, enhancement, protective, making friends, social, and values), the authors tested hypotheses derived from socioemotional selectivity theory regarding the effects of age on these volunteer motives. The Volunteer Functions Inventory was completed by 523 volunteers from 2 affiliates of the International Habitat for Humanity. Multiple regression analyses revealed, as predicted, that as age increases, career and understanding volunteer motivation decrease and social volunteer motivation increases. Contrary to expectations, age did not contribute to the prediction of enhancement, protective, and values volunteer motivations and the relation between age and making friends volunteer motivation was nonlinear. The results were discussed in the context of age-differential and age-similarity perspectives on volunteer motivation.