Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof

This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢_GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢_PA S^ξ and d(S, G) > 0 imply the inconsistency of PA. This revised version was published online in June 2006 with corrections to the Cover Date.     

An Operational Logic of Proofs with Positive and Negative Information

The logic of proofs was introduced by Artemov in order to analize the formalization of the concept of proof rather than the concept of provability. In this context, some operations on proofs play a very important role. In this paper, we investigate some very natural operations, paying attention not only to positive information, but also to negative information (i.e. information saying that something cannot be a proof). We give a formalization for a fragment of such a logic of proofs, and we prove that our fragment is complete and decidable.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

COMPETITION BETWEEN POSITIVE AND NEGATIVE REINFORCEMENT IN THE TREATMENT OF ESCAPE BEHAVIOR

We compared the effects of reinforcing compliance with either positive reinforcement (edible items) or negative reinforcement (a break) on 5 participants' escape-maintained problem behavior. Both procedures were assessed with or without extinction. Results showed that compliance was higher and problem behavior was lower for all participants when compliance produced an edible item rather than a break. Treatment gains were achieved without the use of extinction. Results are discussed regarding the use of positive reinforcement to treat escape behavior.     

母亲积极养育行为对儿童顺从行为的早期预测与双向作用:从婴儿到学步儿

顺从是儿童早期重要的社会化成就。传统理论关注父母控制策略对顺从的作用,但实证结果表明其解释率有限;当前理论更加关注积极养育行为在顺从发展中具有发展适宜性的作用机制。本研究采用追踪设计考察了84个家庭从儿童6个月到3岁时母亲的敏感性和鼓励自主两种积极养育行为与学步儿顺从发展的关系。结果表明:(1)1岁前母亲敏感性对学步儿2岁时的合作性顺从有正向预测作用,对2岁到3岁合作性顺从的变化没有预测作用;(2)1岁前母亲敏感性对学步儿2岁时的情境性顺从和2岁到3岁的情境性顺从的变化均有负向预测作用;(3)在2岁到3岁期间,母亲的鼓励自主与学步儿的合作性顺从水平有双向正向预测作用,但与情境性顺从不存在双向预测关系。     

对中国宗教及其积极社会功能的正面认识

本文为2011年度中国宗教研究五十人论坛的命题文章,仅对中国宗教及其积极的社会功能作正面探讨。限于篇幅,简要探讨了什么是中国宗教,中国宗教三元并存的格局,中国宗教的包容风格,中国宗教的组织原则,中国宗教扮演的经济角色,中国宗教是多神教,中国人宗教信仰的功利性等问题。     

On Revising Fuzzy Belief Bases

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from “crisp” base revision, as embodied by the idea of partial meet (base) revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy base revision and illustrate how the operation works in several important special instances of the framework. We also axiomatise the related operation of partial meet fuzzy base contraction.This paper is an extended version of a paper presented at the Nineteenth Conference on Uncertainty in Arti.cial Intelligence (UAI’03).     

Logic and Philosophy of Logic in Wittgenstein

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of logic contains many interesting thoughts that have gone widely unnoticed.     

Sweet-cheeks vs. pea-brain: embodiment,valence, and task all influence the emotional salience of language

Previous research has found that more embodied insults (e.g. numbskull) are identified faster and more accurately than less embodied insults (e.g. idiot). The linguistic processing of embodied compliments has not been well explored. In the present study, participants completed two tasks where they identified insults and compliments, respectively. Half of the stimuli were more embodied than the other half. We examined the late positive potential (LPP) component of event-related potentials in early (400–500?ms), middle (500–600?ms), and late (600–700?ms) time windows. Increased embodiment resulted in improved response accuracy to compliments in both tasks, whereas it only improved accuracy for insults in the compliment detection task. More embodied stimuli elicited a larger LPP than less embodied stimuli in the early time window. Insults generated a larger LPP in the late time window in the insult task; compliments generated a larger LPP in the early window in the compliment task. These results indicate that electrophysiological correlates of emotional language perception are sensitive to both top-down and bottom-up processes.     

Wisdom at the end of life: Hospice patients’ reflections on the meaning of life and death

The processes of aging and confronting mortality are often accompanied by unique psychological challenges. From the perspective of positive psychology, such challenges can yield opportunities for growth, including increased wisdom. This qualitative study explored 15 terminally ill hospice patients’ perspectives on wisdom, the dying process, and the meaning of life using consensual qualitative research methods. Most participants cited humility as a key component of wisdom, emphasizing that “Wisdom is when we realize ‘I don’t really know much’.” Other components of wisdom included self-knowledge, rationality, experiential learning, listening to and learning from others, and sharing knowledge with others. Participants also suggested that the process of facing illness and death presents opportunities for positive growth, including changing priorities and learning to appreciate life more fully in the present moment. In considering the sources of meaning in their lives, participants emphasized relational connections, personal growth, spirituality, vocational fulfilment, and living a full life. Participants also shared their reflections on important past experiences and regrets. Lastly, participants offered advice to others based on their experiences facing illness and mortality. Implications for psychological care of the dying and future research are discussed.