The Logic of Knowledge Based Obligation

Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty. Earlier versions of this paper were presented at the conferences SEP-2004, and DALT-2004.     

Conditional Probability and Defeasible Inference

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. The research of both authors was supported in part by a grant from NSF, and, for Parikh, also by support from the research foundation of CUNY.     

Factors Related to Play Therapists' Social Justice Advocacy Attitudes

The authors used a correlational research design to examine how belief in a just world, political ideology, socioeconomic status of family of origin, and percentage of racial minority clients were related to social justice advocacy attitudes among play therapists. A multiple regression was used to analyze the data. Results indicated that belief in a just world and political ideology were related to social justice advocacy. Implications for play therapy training and future directions for research are discussed. Los autores emplearon un diseño correlacional de investigación para examinar cómo la creencia en un mundo justo, la ideología política, el estatus socioeconómico de la familia de origen y el porcentaje de clientes de minorías raciales estaban relacionados con actitudes de apoyo de la justicia social entre consejeros que usan terapia de juego. Se empleó una regresión múltiple para analizar los datos. Los resultados indicaron que la creencia en un mundo justo y la ideología política estaban relacionadas con la defensa de la justicia social. Se discuten las implicaciones para formación en terapia de juego y direcciones futuras para investigación.     

Beth definability,interpolation and language splitting

Both the Beth definability theorem and Craig’s lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L ₁ with another language L ₂, that is to say, information transfer—or the lack of such transfer—between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo. Section 3 does contain one apparently new theorem.     

Radical Semantics: A New Theory of Meaning

This paper extends Parikh’s earlier work in semantics with games of partial information and attempts to derive and represent the full content of an utterance from first principles. It also discusses various ways in which this content may be indeterminate.     

Completeness of Certain Bimodal Logics for Subset Spaces

Subset Spaces were introduced by L. Moss and R. Parikh in [8]. These spaces model the reasoning about knowledge of changing states.In [2] a kind of subset space called intersection space was considered and the question about the existence of a set of axioms that is complete for the logic of intersection spaces was addressed. In [9] the first author introduced the class of directed spaces and proved that any set of axioms for directed frames also characterizes intersection spaces.We give here a complete axiomatization for directed spaces. We also show that it is not possible to reduce this set of axioms to a finite set.     

Cognitive Behavioral Therapy for Bariatric Surgery Patients: Preliminary Evidence for Feasibility,Acceptability, and Effectiveness

Bariatric surgery is the most effective treatment for extreme obesity; however, 20% to 50% of patients begin to regain their weight within the first 1.5 to 2 years following surgery. Despite some psychosocial factors predicting postoperative weight loss and weight regain, psychosocial interventions are not routinely offered in bariatric surgery programs. In this paper, we describe a 6-session cognitive behavioral therapy (CBT) intervention for preoperative and postoperative bariatric surgery patients with maladaptive eating behaviors or thought patterns, which can be delivered either in person or by telephone. In addition, we describe a small pilot study (n = 8) designed to examine the feasibility and acceptability of the CBT intervention, as well as its effectiveness in improving eating pathology and psychosocial functioning. Most pilot study participants reported improvements in binge eating severity, emotional eating, and depression from pre- to posttreatment, and all participants provided positive qualitative feedback regarding the intervention.