College Student Depression: Counseling Billy

A substantial portion of the college student population experiences affective disorders. This case study presents the conceptualization, course of treatment, and outcomes for a male college student presenting for counseling with depression. A review of Adlerian, cognitive-behavioral, and Gestalt techniques is provided

Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

MAGPIES: Math & Girls + Inspiration = Success: Creating and Implementing a Virtual Math Circle for Girls

During the academic year 2020-2021, we ran a virtual math outreach program for upper elementary and middle school girls, MAGPIES: Math & Girls + Inspiration = Success. Monthly sessions were held over Zoom, beginning with a short introduction by a guest presenter, followed by breakout rooms led by undergraduates paired with more experienced facilitators (upper division and graduated math majors and volunteer math educators). The online community was created purposefully to be an inclusive and collaborative environment for the attending girls, and the lessons were designed to provide a learning experience for all levels of participants. Examples of sessions include Mathematics and Voting and a mathematical exploration of the card game SET®. Math major coordinators contributed to MAGPIES in numerous ways, such as helping to develop materials, running the Zoom sessions, social media management and website development. We held training sessions prior to each workshop, which consisted of preparing volunteers to use the tools of Zoom (e.g., breakout rooms, chat, annotation, whiteboard), as well as introducing the mathematics and the specifics of the lesson plan. In this article, we illustrate the impacts of this program by focusing on the voices of the community members who have been with us for significant portions of the MAGPIES journey

Practical Reasoning for Very Expressive Description Logics

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems

Linguistic Mechanisms Cause Rapid Behavior Change Part Two: How Linguistic Frames Affect Motivation

Written and spoken language contains inherent mechanisms driving motivation. Accessing and modifying psycholinguistic mechanisms, links language frames to changes in behavior within the context of motivational profiling. For example, holding an object like an imported apple feels safe until one is informed it was grown in a toxic waste dump. Instantly linguistic processing changes the apple’s meaning to dangerous. Qualitative data change from static into dynamic measures of motivational changes. Linguistic cause-effect mechanisms dramatically enhance the results and meaning of qualitative research methods, resulting new applications for behavioral engineering, including opinion polling, persuasive marketing campaigns, individual psychotherapy and executive performance coaching. Motivational mechanisms, especially linguistic frames, engineer deliberate and predictable improvements in outcomes, impossible with popular statistical methods

How Linguistic Frames Affect Motivational Profiles and the Roles of Quantitative versus Qualitative Research Strategies

The combined tools of psycholinguistics and systems analysis have produced advances in motivational profiling resulting in numerous applications to behavioral engineering. Knowing the way people frame their motive offers leverage in causing behavior change ranging from persuasive marketing campaigns, forensic profiling, individual psychotherapy, and executive performance. Professionals study motivation in applied or theoretical settings, often with strong implicit biases toward either quantitative or qualitative strategies. Many experts habitually frame behavioral research issues with ill-fitting quantitative and qualitative strategies. The third strategic choice offered here is state-of -the -art, psycholinguistic communications modeling. The role of these research strategies is explored

A Quantitative Extension of Interval Temporal Logic over Infinite Words

Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHSsimple of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHSsimple, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Hedging Our Bets: Why Does Nuclear Latency Matter?

The article of record as published may be located at https://doi.org/10.1080/0163660X.2019.1592363Funded by Naval Postgraduate SchoolSince the dawn of the nuclear age, only 10 states have successfully obtained nuclear weapons. Out of 195 countries in the world today, that is quite a small number. Beyond those 10, however, a relatively larger number of 32 states, at one time or another, have had what is known as a nuclear latent capacity. Technically speaking, latency is a state’s possession of either an operational uranium enrichment or plutonium reprocessing capability—the two pathways that can yield the critical material for nuclear bombs or civilian nuclear energy generation. More generally, we consider latent states to be those who have this technological capability but have yet to use it to acquire nuclear weapons.This work results from research sponsored by the Naval Postgraduate School’s Project on Advanced Systems and Concepts for Countering WMD, with funding from the Defense Threat Reduction Agency, under Assistance Grant/Agreement No. N00244- 16-1-0042 awarded by the NAVSUP Fleet Logistics Center San Diego.This work results from research sponsored by the Naval Postgradu- ate School’s Project on Advanced Systems and Concepts for Countering WMD, with funding from the Defense Threat Reduction Agency, under Assistance Grant/Agreement No. N00244- 16-1-0042 awarded by the NAVSUP Fleet Logistics Center San Diego