Decomposition Proof Systems for Gödel-Dummett Logics

The main goal of the paper is to suggest some analytic proof systems for LC and its finite-valued counterparts which are suitable for proof-search. This goal is achieved through following the general Rasiowa-Sikorski methodology for constructing analytic proof systems for semantically-defined logics. All the systems presented here are terminating, contraction-free, and based on invertible rules, which have a local character and at most two premises.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

The logic of ability,freedom and responsibility

The aim of this paper is to offer a rigorous explication of statements ascribing ability to agents and to develop the logic of such statements. A world is said to be feasible iff it is compatible with the actual past-and-present. W is a P-world iff W is feasible and P is true in W (where P is a proposition). P is a sufficient condition for Q iff every P world is a Q world. P is a necessary condition for Q iff Q is a sufficient condition forP. Each individual property S is shown to generate a rule for an agent X. X heeds S iff X makes all his future choices in accordance with S. (Note that X may heed S and yet fail to have it). S is a P-strategy for X iff X's heeding S together with P is a necessary and sufficient condition for X to have S. (P-strategies are thus rules which X is able to implement on the proviso P).Provisional opportunity: X has the opportunity to A provided P iff there is an S such that S is a P-strategy for X and X's implementing S is a sufficient condition for X's doing A. P is etiologically complete iff for every event E which P reports P also reports an etiological ancestry of E, and P is true. Categorical opportunity: X has the opportunity to A iff there is a P such that P is etiologically complete and X has the opportunity to A provided P. For X to have the ability to A there must not only be an appropriate strategy, but X must have a command of that strategy. X steadfastly intends A iff X intends A at every future moment at which his doing A is not yet inevitable. X has a command of S w.r.t. A and P iff X's steadfastly intending A together with P is a sufficient condition for X to implement S. Provisional ability: X can A provided P iff there is an S such that S is a P-strategy for X, X's implementing S is a sufficient condition for X's doing A, and X has a command of S w.r.t. A and P. Categorical ability: X can A iff there is a P such that P is etiologically complete and X can A provided P. X is free w.r.t. to A iff X can A and X can non- A. X is free iff there is an A such that X is free w.r.t. A.     

Valuation Semantics for First-Order Logics of Evidence and Truth

This paper introduces the logic QLET_F, a quantified extension of the logic of evidence and truth LET_F, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LET_F is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A’s violating some classically valid inferences. The semantics of QLET_F combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics.

     

Knowledge despite falsehood

I examine the claim, made by some authors, that we sometimes acquire knowledge from falsehood. I focus on two representative cases in which a subject S infers a proposition q from a false proposition p. If S knows that q, I argue, S's false belief that p is not essential to S's cognition. S's knowledge is instead due to S's belief that p′, a proposition in the neighbourhood of p that S (dispositionally) believes (and knows). S thus knows despite her false belief. The widely accepted and plausible principle that inferential knowledge requires known premises is unscathed.     

A Statistical Hypothesis Testing Method for the Rank Ordering of the Priorities of the Alternatives in the Analytic Hierarchy Process

In analytic hierarchy process (AHP), a ratio scale (π₁, π₂, ⋯, π_t) for the priorities of the alternatives {T₁, T₂, ⋯, T_t} is used for a decision problem in which π_i/π_j is used to quantify the ratio of the priority of T_i to that of T_j. In a group decision‐making setup, the subjective estimates of π_i/π_j are obtained as entries of a pairwise comparison matrix for each member of the group. On the basis of these pairwise comparison matrices, one of the topics of interest in some situation is the total rank ordering of the priorities of the alternatives. In this article, a statistical method is proposed for testing a specific total rank ordering of the priorities of the alternatives. The method developed is then illustrated using numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Kant,the Third Antinomy and Transcendental Arguments

In this paper, I consider whether a reading of Kant's solution to the Third Antinomy can offer material for devising a new model of transcendental argument. The problem that this form of argument is meant to address is an antinomy between two apparently contradictory claims, q and ¬q, where we seem equally justified in holding both. The model has the following form: p; q is a necessary condition of p; the only justification we have for q is that it is a necessary condition of p; p is justified only in domain X (where X is a domain of objects of cognition); therefore, q is justified only in domain X. Because the argument shows that our justification for q is valid only in X, it also establishes that there is conceptual space to hold ¬q outside of X.     

Some general laws of human emotion: Interrelationships between intensities of desire, expectation, and emotional feeling

Two experiments were performed to determine how desires and expectations interact to influence the intensities of emotional feelings. The first experiment required participants to respond to their imagined intensities of desire and expectation in two hypothetical situations, (1) anticipating different probabilities of receiving money (2) anticipating the possibility of different durations of continuous rain combined with different probabilities of rain occurring. Participants responded by producing line lengths to desire and feeling, a form of cross-modality matching. Feeling intensity but not desire intensity increased as a negatively accelerating power function of expectation for the positive approach goal of receiving money (F =KE^0.5) and both desire and feeling were negatively accelerating power functions of the hypothetical amount of money presented (F=K$⁴; D=K$⁴). Feeling intensity but not desire intensity increased as a positively accelerating function of expectation for the negative avoidance goal of anticipating different amounts of rain (F=KE^1.9) and both desire and feeling were negatively accelerating functions of amount of rain (F=KR^0.9; D=KR_0.9). The second experiment required participants to make visual analogue scale responses to desire, expectation, and emotional feeling intensities in ordinary life situations. Similar to Experiment 1, feeling intensity but not desire intensity increased as a negatively accelerating function of expectation for positive approach goals (F=KE^0.6) and as a positively accelerating function of expectation for negative avoidance goals (F=KE^2.0). Functional interrelationships found in both experiments were fit to the general equations F=K₁D+K₂DE^0.5 for positive approach goals and F=K₁D+K₂DE^2.0 for negative avoidance goals. Both equations have the same general form and indicate that desire and expectation have a multiplicative interaction with respect to their influence on emotional feeling intensity. Both functions     

An Affordance-Based Approach to Visually Guided Overtaking

When an automobile driver overtakes a lead vehicle while avoiding oncoming traffic, does he or she do so with reference to the limits of his or her car? We investigated overtaking from the perspective of the theory of affordances. We define the overtake-ability affordance as a ratio of the minimum satisfying velocity required for safe overtaking (MSV) to the maximum velocity of the driver's car (V_max). Two groups of participants performed overtaking maneuvers, if deemed possible, by driving either a slow (V_max = 25 m/s) or a fast (V_max = 32.5 m/s) virtual car in overtaking situations constrained by 14 values of MSV. For any given MSV condition, participants in the fast car group were more likely to attempt an overtaking maneuver. However, when MSV was expressed in intrinsic units as a ratio of V_max for both groups, the frequency of overtaking was not significantly different across groups. Furthermore, overtaking frequency dropped to near 0% for both groups when MSV exceeded V_max. In accordance with the affordance-based framework (Fajen, 2007), our results suggest that participants select their overtaking maneuvers by perceiving an overtake-ability affordance.     

A Five‐dimensional Model of Attributes: Some precursors of executive coach selection

The purpose of this study was to specify a set of attributes, identified as important precursors to coach selection. Executive coaching has grown exponentially, but there have been few studies as to the efficacy of coaching, including the factors that influence a manager's choice of coach. This study sought to identify these factors. The 45‐item, online survey produced 267 useable responses. Results of the principal component analysis suggested a five‐factor solution, with women showing a statistically significant preference over men for coaches who have the Ability to Develop Critical Thinking and Action, the Ability to Forge the Coaching Partnership and Coach Experience and Qualifications. The impact of coachee age was not significant in selecting executive coaches. The findings show a statistically significant relationship between coach attributes and the intention to continue with coaching. The implications of these findings for the selection of coaches, and for the coaching profession are discussed.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

Peer Influence in Elementary School: The Importance of Assessing the Likeability of Popular Children

Abstract

We examined the degree to which children perceive influence behaviors and influence over social norms from different types of high-status children to vary in a sample of 453 3^rd through 5^th grade children. Using a cluster analysis of peer-nominated popularity and likeability measures, we identified a seven-cluster solution, including three high-status clusters: Well-Liked, Popular, and Popular/Well-Liked. Popular children were perceived as using ridicule and having influence over misbehavior. Popular/Well-Liked children were perceived as using playful teasing and modeling and influencing over trend-setting and sports norms, at a degree similar to Popular children. However, Popular/Well-Liked children were not perceived as using ridicule or influencing over misbehavior; rather, they scored higher than all other status groups for prosocial assertion and academic motivation. Well-Liked children were perceived as using prosocial assertion and influencing over academic motivation at a higher degree than Average children but at a lower degree than Popular or Popular/Well-Liked children. Although the influence associated with likeability alone appeared relatively limited, likeability in conjunction with popularity seems to make a difference regarding influence behaviors and norms. A person-centered approach that takes into account multiple facets of social status is likely to enhance understanding of high-status children’s influence on their same-age peers.     

Henkin Quantifiers and the Definability of Truth

Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension L _* ¹(H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close L _* ¹(H) with respect to Boolean operations, and obtain the language L ¹(H). At the next level, we consider an extension L _* ²(H) of L ¹(H) in which every sentence is an L ¹(H)-sentence prefixed with a Henkin quantifier. We repeat this construction to infinity. Using the (un)-definability of truth – in – N for these languages, we show that this hierarchy does not collapse. In addition, we compare some of the present results to the ones obtained by Kripke (1975), McGee (1991), and Hintikka (1996).     

Development and Evaluation of a Decision Aid About Prenatal Testing for Women of Advanced Maternal Age

Objective: To develop and evaluate a decision aid designed to prepare patients of advanced maternal age for counseling about prenatal diagnostic testing. Setting: A regional genetics center. Design: A before/after study. Interventions: Participants used an audioguided workbook to learn about options and outcomes and to clarify personal risks, values, questions, and predispositions. Subjects: 21 women of advanced maternal age and 17 spouses. Main outcome measures: Knowledge of prenatal testing alternatives, decisional conflict, level of anxiety, and acceptability of the decision aid. Results: After using the decision aid, participants had significantly reduced decisional conflict (uncertainty) and a significant increase in knowledge. There was no effect on state or trait anxiety. More than three-quarters of participants were satisfied with the length, clarity, balance, and acceptability of the decision aid. Conclusions: The decision aid shows promise as a useful aid for preparing couples for counseling.     

The requirements of truth and of justification of premisses

Summary The article attempts to give an answer to the question: why for the acceptance of a statementz ₂ implied by another,z ₁, it is required not only thatz ₁ be true but also justified? The application in a given case of the rule allowing to accept a statement implied by another true one is not possible without establishing in an appropriate manner that the statement is true. Practically, therefore, we have to rely in the conditions for the acceptance of a statementz ₂ implied by anotherz ₁ on the manner of acceptance ofz ₁. If we require that this manner of acceptance should guarantee the truth ofz ₁, no special requirement of the truth ofz ₁ is necessary. If the acceptance ofz ₂ implied byz ₁ depends onz ₁ being accepted in a manner which does not ensure the truth ofz ₁ (e. g. by induction), then we have to give up the requirement of the truth ofz ₁. At most, we may prohibit the acceptance ofz ₂ implied byz ₁, inductively justified, if the evidence for the negation ofz ₁ is better than the inductive one forz ₁.     

Conditional probability judgments: Effects of imagining vs experiencing the conditioning event

Applications of Bayesian conditionalization often involve two temporal aspects: a probability judgment is based on knowledge at a point in time and is revised over time in light of added information. Let t, t′, and t″ designate three chronological points in time. E designates a target event which occurs or not at t″, and C designates a conditioning event which occurs or not at t′. Suppose that an individual judges P(EC) at t. If C occurs, Bayesian conditionalization requires that a judgment of P(E) at t′ is equal to the earlier judgment of P(EC). However, inconsistencies may result because a judgment of P(EC) at t is based on imagining C, while a judgment of P(E) at t′ is based on experiencing C. This study examines two sources of such inconsistencies. First, C normally is an abstraction of what might happen between t and t′. What actually happens may differ, such that an individual observes extraconditional information which affects a judgment of P(E) at t′. Second, experiencing C may change an individual's affective state, leading to greater optimism or pessimism about the occurrence of E. We report an experiment which documents both effects.     

Calibrating Study and Learning as Hermeneutic Principles Through Greco-Christian Seeing,Rabbinic Hearing,and Chinese Yijing Observing

Study is recently re-invoked as an alternative educational formation to disrupt the learning trap and trope. This paper calibrates study and learning as two hermeneutic principles and correlates them with seeing, hearing, and observing as three onto-epistemic modes that respectively underpin Greco-Christian, Rabbinic, and ancient Chinese exegetical traditions. Linking study and learning with the hermeneutic issues of language, text, meaning, and reality, my calibration unfolds in four steps. First, I introduce an epistemic aporia encountered in interpreting some Chinese educational “wind” texts, exposing our naturalized reasoning of learning along a representational enclosure. Second, turning to Susan Handelman’s writing, I trace this learning-as-representation enclosure as being conditioned upon the Greco-Christian exegetical mode of seeing, meanwhile correlating study back with the Rabbinic hearing hermeneutic. Third, I move on to explicate an onto-cosmological Yijing observing, proffering a study hermeneutic as a movement of observing, following, and attuning to wendao, literally put, “a crisscrossing pattern that (re-)turns with dao.” Finally, I re-observe and study the crisscrossing Chinese educational “wind” texts, evoking a Chinese “wind-teaching” sensibility so far rarely discerned through representational thinking and learning.

     

A Logic for Multiple-source Approximation Systems with Distributed Knowledge Base

The theory of rough sets starts with the notion of an approximation space, which is a pair (U,R), U being the domain of discourse, and R an equivalence relation on U. R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U. The focus then is on approximations of concepts on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base, which is a tuple (U,R_P)_{Pßf N}(U,R_P)_{P\ss_f N}, where N is a set of sources and P ranges over all finite subsets of N. Each R _P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS ^D is proposed. In LMSAS ^D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS ^D are discussed and it is shown that the modal system KTB is embedded in LMSAS ^D . The epistemic logic S5^D_nS5^D_n is also embedded in LMSAS ^D , and cannot replace the latter to serve our purpose. The relationship of LMSAS ^D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed.     

One Aspect of Hartmann's Review of Human Nature and Enduring Peace

Summary

Eighty Negro boys and girls, ages 3 to 5, were assigned to one of eight conditions. Race of model (Negro vs. white), type of consequence to model (reward vs. punishment), and percent of rewarded or punished responses (20 vs. 80 percent) were varied. The Ss viewed a television tape of a model (M) performing a simple two-choice discrimination task with either verbal reward or verbal punishment administered. After watching M make his choice, the S then made his own choice. When S's choice was the same as M's, imitative behavior was said to have occurred. There were significant effects of both race of M and type of consequence to M. Negro S imitated the white M more than the Negro M and imitated the rewarded M more than the punished M. The punished white M was imitated at approximately the same level as the rewarded Negro M. No significant effects of percent of reinforcement were found. Possible explanations of the experimental results were discussed.     

Restricted ranking

This paper is a study of certain aspects of restricted ranking, a method intended for use by a panel ofm judges evaluating the relative merits ofN subjects, candidates for scholarships, awards, etc. Each judge divides theN subjects intoR classes so thatn _i individuals receive a gradei (i = 1, 2, ...,R; Σn _i =N) where theR numbersn _i are close toN/R (n _i =N/R whenN is divisible byR) and are preassigned and the same for all judges. This method is superior in several respects to other likely alternatives. Under the null hypothesis that allnR =N subjects are of equal merit, four tests of significance are developed. The effectiveness of the method is investigated both theoretically by means of the asymptotic relative efficiency and more generally by simulation studies. When the numbersn _i are not restricted to values close to or equal toN/R but instead are given values conforming to a normally distributed pattern, the resulting method is known as theQ-sort, so designated by certain investigators in psychotherapy. The simulation studies reveal that restricted ranking is only slightly inferior to complete ranking and generally superior in the cases considered to theQ-sort, although there are likely to be other situations when the latter is superior. The authors are indebted to Dr. Clyde Kramer of Virginia Polytechnic Institute for bringing theQ-sort ranking technique of psychotherapy to their attention.