Hypothetical Actions Research Articles

The Mediation Proportion

To the Editor: We read with interest the recent article by Ditlevsen and colleagues1 on effect decomposition using structural equations models (SEM) in epidemio logic research. Every few years an arti cle appears in an epidemiology journal encouraging greater use of path analysis or SEM methods (eg, Susser et al2), but Ditlevsen et al provide several develop ments of particular interest to epidemi ologists. For example, they compare the SEM approach with some of the existing statistical literature on surrogate out comes, and also describe a model of binary outcomes as realized manifesta tions of latent continuous variables. Unfortunately, the article over looks some important developments in effect definition and decomposition over the last 20 years, as presented else where.36 In particular, Ditlevsen et al provide no interpretation for their pa rameters in terms of an underlying for mal causal model. Indeed, the strategy of focusing attention on an arbitrarily scaled latent continuous variable makes it difficult to give causal interpretations to the estimated regression coefficients or to the mediation proportion derived from these coefficients.7 Furthermore, because of identification problems, a variety of causal structures can give rise to the same value for parameters such as the mediation proportion, even when the causal implications of these various structures would be entirely different.6 Finally, for many epidemiologic out comes (eg, spontaneous abortion or mortality), focusing attention on the causal effect of the exposure on the latent continuous outcome, rather than on the observed discrete event, seems to lack clear public-health meaning. When examined in terms of poten tial outcomes, the restrictive assump tions used by Ditlevsen et al (linearity and additivity) can be shown to still be insufficient to give the mediation pro portion an unambiguous causal interpre tation; this interpretation would require the additional assumption of no interac tion at the unit level.8 Under a more general set of circumstances, the total effect (defined causally as a contrast of hypothetical actions) will not decom pose additively into direct and indirect effects.46 In these settings it may still be feasible and substantively interesting to estimate total and direct causal ef fects, recognizing that the latter can be greater than or in the direction opposite to the former.4-6

Supervised Learning Through Neuronal Response Modulation

Neural networks that are trained to perform specific tasks must be developed through a supervised learning procedure. This normally takes the form of direct supervision of synaptic plasticity. We explore the idea that supervision takes place instead through the modulation of neuronal excitability. Such supervision can be done using conventional synaptic feedback pathways rather than requiring the hypothetical actions of unknown modulatory agents. During task learning, supervised response modulation guides Hebbian synaptic plasticity indirectly by establishing appropriate patterns of correlated network activity. This results in robust learning of function approximation tasks evenwhenmultiple output units representing different functions share large amounts of common input. Reward-based supervision is also studied, and a number of potential advantages of neuronal response modulation are identified.

Self-Strengthening Empathy

Stepping into the other guy's shoes works best when you resemble him. After all, the procedure is to use yourself as a model: in goes hypothetical beliefs and desires, out comes hypothetical actions and revised beliefs and desires. If you are structurally analogous to the empathee, then accurate inputs generate accurate outputs-just as with any other simulation. The greater the degree of isomorphism, the more dependable and precise the results. This sensitivity to degrees of resemblance suggests that the method of empathy works best for average people. The advantage of being a small but representative sample of the population will create a bootstrap effect. For as average people prosper, there will be more average descendants and so the degree of resemblance in subsequent generations will snowball. Each increment in like-mindedness further enhances the reliability and validity of mental simulation. With each circuit along the spiral, there is tighter and tighter bunching and hence further empowerment of empathy. The method is self-strengthening and eventually molds a population of hyper-similar individuals-which partly solves the problem of other minds.

Intuitionistic deductive databases and the polynomial time hierarchy

Deductive databases are poor at tasks such as planning and design, where one must explore the consequences of hypothetical actions and possibilities. To address this limitation, we have developed a deductive database language in which a user can create hypotheses and draw inferences from them. In earlier work, we established initial results on the complexity and expressibility of this language. In this paper, we establish more comprehensive results by exploring the interaction of negation-as-failure with a natural syntactic restriction called linearity. The main result is a tight connection between intuitionistic logic, database queries, and the polynomial time hierarchy. A tight connection with second-order logic follows as a corollary. First, we show that rulebases in our language fit neatly into a well-established logical framework— intuitionistic logic. Second, we show that linearity reduces their data complexity from PSPACE to NP. Third, we show that negation-as-failure increase their complexity from NP to some level in the polynomial time hierarchy (PHIER). Specifically, linear rulebases with k strata are data complete for ∑ k P, the kth level in the hierarchy. Fourth, we show that linear rulebases express exactly the generic database queries in PHIER. Finally, we characterize the generic queries in ∑ k P in terms of rulebases with k strata. Unlike many other expressibility results in the literature, these results do not depend on the artificial assumption that the data domain is linearly ordered. We thus establish a strong link between two well-established, but previously unrelated areas: intuitionistic logic and the polynomial time hierarchy.

A logical semantics for hypothetical rulebases with deletion

This paper addresses a limitation of most deductive database systems: they cannot reason hypothetically. Although they reason effectively about the world as it is, they are poor at tasks such as planning and design, where one must explore the consequences of hypothetical actions and possibilities. To address this limitation, we have developed a logic-programming language in which users can create hypotheses and draw inferences from them. Most previous work in this area has focused on the hypothetical insertion of facts into a database since insertion is accounted for by a well-established logic: intuitionistic logic. In contrast, our language includes hypothetical deletion as well as insertion. In earlier work, we established the data complexity and expressibility of this language. In this paper, we develop its logical semantics, and take a closer look at its expressibility. The paper makes three main contributions. First, we show that hypothetical queries lead naturally to a new notion of expressibility. In this new light, we show that classical logic is poor at hypothetical reasoning since it cannot express some simple hypothetical queries. Second, we develop a logical semantics for hypothetical insertions and deletions, including a proof theory, model theory, and fixpoint theory. We also give numerous examples showing the utility of the logic and the subtle effect that deletion has on its expressive power. Finally, we augment the logic with negation-as-failure so that nonmonotonic queries can be expressed. We then develop the proof theory and model theory for the logic with negation. The proof theory is inspired by the stratified semantics of Apt, Blair, and Walker, and the model theory is inspired by the perfect model semantics of Przymusinski.

Metalización de medidas de corrección de la intrusión marina en los acuíferos de río Vélez, río Verde y Castell de Ferro (provincias de Málaga y Granada)

The sea water intrusion process shows different dynamics in three spanish southmediterranean coastal aquifers affected by seasonal overexploitation (Rio Velez, Rio Verde and Castell de Ferro). On the base of these differences we carried out a mathematical modeling to check the effectiveness of severa1 hypothetical actions against this contaminant process. For the Rio Velez aquifer we have modeled first of al1 a total omission of flow in the river during the wet season. We conclude the sea water intrusion should be not affected noticeably. Second of al1 we have simulated a certain flow in the river during the whole year, which should reduce markedly the volume of sea water intruding this aquifer. The modeling for the Rio Verde aquifer shows that an artificial recharge (using resources from neighbouring basins) during the wet season is not an efficient action against sea water intrusion. During the dry season it should be more efficient against contamination to use the imported resources directly for irrigation than using then to recharge the system. Finally, an hypothetical stoppage of pumping in the Castell the Ferro aquifer should make sea water intrusion to disappear, but should not be efficient to wash remaining salts. So, we have simulated as well the effect of a low permeability barrier located between the detrital materials and a karstified block connected to the sea as well. This action appears as an interesting one as it should reduce the volume of sea water intrusion and inducing to an increase of seaward flow through the detrital materials, giving way to a good washing of salts.

HYPOTHETICAL REASONING ABOUT ACTIONS: FROM SITUATION CALCULUS TO EVENT CALCULUS

Hypothetical reasoning about actions is the activity of preevaluating the effect of performing actions in a changing domain; this reasoning underlies applications of knowledge representation, such as planning and explanation generation. Action effects are often specified in the language of situation calculus, introduced by McCarthy and Hayes in 1969. More recently, the event calculus has been defined to describe actual actions, i.e., those that have occurred in the past, and their effects on the domain. Altough the two formalisms share the basic ontology of atomic actions and fluents, situation calculus cannot represent actual actions while event calculus cannot represent hypotethical actions. In this article, the language and the axioms of event calculus are extended to allow representing and reasoning about hypothetical actions, performed either at the present time or in the past, altough counterfactuals are not supported. Both event calculus and its extension are defined as logic programs so that theories are readily adaptable for Prolog query interpretation. For a reasonably large class of theories and queries, Prolog interpretation is shown to be sound and complete w.r.t. the main semantics for logic programs.

From Cost-Perception to Gain-Construction: Toward a Piagetian Explanation of the Development of Altruism in Children

This study provides some data to help explain the development of altruism in children in accordance with a theoretical perspective which integrates the two micromodels Piaget used successively to account for the child's transition from intuitive or preoperational to reversible or operational thought. One of those models is guided by games theory and involves a cost-gain evaluation. The other is based on equilibration theory, and hence on the priority of affirmation over negation before the child attains the compensatory equilibrium of operational logic. On the basis of this theoretical perspective, it is hypothesised that children are more likely with age to consider altruistic acts in terms of gain-gain-construction than in terms of cost-cost-perception. Ninety children (30 5-6 years old, 30 8-9 years old, and 30 11-12 years old) were individually tested. They listened to a story describing two hypothetical actions: one altruistic (comforting), the other egoistic (not comforting). Children were then asked some questions concerning their cost-perception/ gain-construction in these actions. Results showed that children were more likely with age to consider the altruistic act in terms of gain-construction (negation) than in terms of cost-perception (affirmation). Although the findings of this research strengthen the possibility of seeing the development of altruism in children in accordance with the two aforementioned Piagetian micromodels, the paper concludes with a cautious interpretation of the results and calls for further empirical and conceptual efforts.