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In this paper we study proof procedures for some variants of first-order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds where they are meant to be interpreted.This paper is an extended version of a previous work where full proofs were not included. Proofs are in some points rather tricky and may help in understanding the reasons for some details in basic definitions.  相似文献   
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Up to 37% of individuals experience chronic pain during their lifetimes. Approximately one-fourth of primary care patients with chronic pain also meet criteria for major depression. Many of these individuals fail to receive psychotherapy or other treatment for their depression; moreover when they do, physical pain is often not addressed directly. Women, socioeconomically disadvantaged individuals, African Americans and Latinos all report higher rates of pain and depression compared to other groups. This article describes a version of Interpersonal Psychotherapy tailored for patients with comorbid depression and chronic pain, Interpersonal Psychotherapy for Depression and Pain (IPT-P). While IPT-P potentially could be delivered to many different patient populations in a range of clinical settings, this article focuses on its delivery within primary care settings for socioeconomically disadvantaged women. Adaptations include a brief 8-session protocol that incorporates strategies for anticipating barriers to psychotherapy, accepting patients' conceptualization of their difficulties, encouraging patients to consider the impact of their pain on their roles and relationships, emphasizing self-care, incorporating pain management techniques, and flexible scheduling. In addition, IPT-P is designed as an adjunct to usual medical pain treatment, and seeks to engage non-treatment seeking patients in psychotherapy by focusing on accessibility and relevance of the intervention to concerns common among patients with pain. Identifying patients with comorbid depression and chronic pain and offering IPT-P as a treatment option has the potential to improve clinical outcomes for individuals with depression and chronic pain.  相似文献   
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