A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems.     

A comparison of stimulus set size on tact training for children with autism spectrum disorder

Previous studies on skill acquisition have taught targets in stimulus sets composed of different numbers of stimuli. Although the rationale for selection of a stimulus set size is not clear, the number of target stimuli trained within a set is a treatment decision for which there is limited empirical support. The current investigation compared the efficiency of tact training in 4 stimulus set sizes, each of which included 12 stimuli grouped into (a) 4 sets of 3 stimuli, (b) 3 sets of 4 stimuli, (c) 2 sets of 6 stimuli, and (d) 1 set of 12 stimuli. Results of all 4 participants with autism spectrum disorder show tact training with larger (i.e., 6 and 12) stimulus set sizes was more efficient than training with smaller (i.e., 3 and 4) stimulus set sizes.     

Compact integer-programming models for extracting subsets of stimuli from confusion matrices

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.     

The Best Question

Journal of Philosophical Logic - Suppose we get a chance to ask an angel a question of our choice. What should we ask to make the most of our unique opportunity? Ned Markosian has shown that the...     

A global optimization approach for generating efficient points for multiobjective concave fractional programs

In this article, we present a global optimization approach for generating efficient points for multiobjective concave fractional programming problems. The main work of the approach involves solving an instance of a concave multiplicative fractional program (W̄). Problem (W̄) is a global optimization problem for which no known algorithms are available. Therefore, to render the approach practical, we develop and validate a branch and bound algorithm for globally solving problem (W̄). To illustrate the performance of the global optimization approach, we use it to generate efficient points for a sample multiobjective concave fractional program. Copyright © 2006 John Wiley & Sons, Ltd.     

准备时间和预先信息对任务切换的影响

两个实验采用任务线索范式,考察了准备时间和预先信息对任务切换的影响。实验1的准备时间为可预测,实验2的为不可预测,以考察准备时间的可预测性对任务切换的影响。以被试执行重复任务、切到任务和切离任务的正确反应时为主要指标,结果：（1）在准备时间可预测和不可预测两种条件下,准备时间和预先信息之间存在显著交互作用。在可预测条件中,重复和切到任务的反应时随着准备时间的增加而减少,但切到代价无显著变化,切离任务的反应时不受准备时间的影响,切离代价表现出反准备效应;不可预测条件下,三种任务的反应时都随着准备时间的增加而减少,但是切到和切离代价表现出反准备效应;（2）切离任务的反应时和代价显著高于切到任务的反应时和代价;（3）在这两种条件下,都没有出现切换代价的准备效应     

A verification framework for agent programming with declarative goals

A long and lasting problem in agent research has been to close the gap between agent logics and agent programming frameworks. The main reason for this problem of establishing a link between agent logics and agent programming frameworks is identified and explained by the fact that agent programming frameworks have hardly incorporated the concept of a declarative goal. Instead, such frameworks have focused mainly on plans or goals-to-do instead of the end goals to be realised which are also called goals-to-be. In this paper, the programming language GOAL is introduced which incorporates such declarative goals. The notion of a commitment strategy—one of the main theoretical insights due to agent logics, which explains the relation between beliefs and goals—is used to construct a computational semantics for GOAL. Finally, a proof theory for proving properties of GOAL agents is introduced. Thus, the main contribution of this paper, rather than the language GOAL itself, is that we offer a complete theory of agent programming in the sense that our theory provides both for a programming framework and a programming logic for such agents. An example program is proven correct by using this programming logic.     

Disjunctive logic programming with types and objects: The DLV system

The paper presents DLV⁺, a Disjunctive Logic Programming (DLP) system with object-oriented constructs, including classes, objects, (multiple) inheritance, and types. DLV⁺ is built on top of DLV (a state-of-the art DLP system), and provides a graphical user interface that allows one to specify, update, browse, query, and reason on knowledge bases. Two strong points of the system are the powerful type-checking mechanism and the advanced interface for visual querying.DLV⁺ is already used for the development of knowledge based applications for information extraction and text classification.