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The use of special operations forces (SOF) in war fighting and peace keeping efforts has increased dramatically in recent decades. A scientific understanding of the reason for this increase would provide guidance as to the contexts in which SOF can be used to their best effect. Ashby's law of requisite variety provides a scientific framework for understanding and analyzing a system's ability to survive and prosper in the face of environmental challenges. We have developed a generalization of this law to extend the analysis to systems that must respond to disturbances at multiple scales. This analysis identifies a necessary tradeoff between scale and complexity in a multiscale control system. As with Ashby's law, the framework applies to the characterization of successful biological and social systems in the context of complex environmental challenges. Here we apply this multiscale framework to provide a control theoretic understanding of the historical and increasing need for SOF, as well as conventional military forces. We propose that the essential role distinction is in the separation between high complexity fine scale challenges as opposed to large scale challenges. This leads to a correspondence between the role SOF can best serve and that of the immune system in complex organisms--namely, the ability to respond to fine-grained, high-complexity disruptors and preserve tissue health. Much like a multicellular organism, human civilization is composed of a set of distinct and heterogeneous social tissues. Responding to disruption and restoring health in a system with highly diverse local social conditions is an essentially complex task. SOF have the potential to mitigate against harm without disrupting normal social tissue behavior. This analysis suggests how SOF might be leveraged to support global stability and mitigate against cascading crises., Comment: 10 pages, 2 figures

We present a non-naive version of the Precautionary (PP) that allows us to avoid paranoia and paralysis by confining precaution to specific domains and problems. PP is intended to deal with uncertainty and risk in cases where the absence of evidence and the incompleteness of scientific knowledge carries profound implications and in the presence of risks of "black swans", unforeseen and unforeseable events of extreme consequence. We formalize PP, placing it within the statistical and probabilistic structure of ruin problems, in which a system is at risk of total failure, and in place of risk we use a formal fragility based approach. We make a central distinction between 1) thin and fat tails, 2) Local and systemic risks and place PP in the joint Fat Tails and systemic cases. We discuss the implications for GMOs (compared to Nuclear energy) and show that GMOs represent a public risk of global harm (while harm from nuclear energy is comparatively limited and better characterized). PP should be used to prescribe severe limits on GMOs.

The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the propositional calculus and Boole's mathematical logic: truth-functional and Boolean feasibility (which turn out to be special cases of probabilistic conditionals). Each probabilistic conditional is quantified by a fractional parameter between zero and one that says whether it is purely affirmative, purely negative, or intermediate in its sense. Conditionals can be specialized further by their content to express factuality and counterfactuality, and revised or reformulated to account for exceptions and confounding factors. The various conditionals have distinct mathematical representations: through intermediate probability expressions and logical formulas, each conditional is eventually translated into a set of polynomial equations and inequalities (with real coefficients). The polynomial systems from different types of conditionals exhibit different patterns of behavior, concerning for example opposing conditionals or false antecedents. Interesting results can be computed from the relevant polynomial systems using well-known methods from algebra and computer science. Among other benefits, the proposed framework of analysis offers paraconsistent procedures for logical deduction that produce such familiar results as modus ponens, transitivity, disjunction introduction, and disjunctive syllogism; all while avoiding any explosion of consequences from inconsistent premises. Several example problems from Goodman and Adams are analyzed. A new perspective called polylogicism is presented: mathematical logic that respects the diversity among conditionals in particular and logic problems in general., Comment: Fixed a few typographical errors

A new computational method is presented to implement the system of deductive logic described by Aristotle in Prior Analytics. Each Aristotelian problem is interpreted as a parametric probability network in which the premises give constraints on probabilities relating the problem's categorical terms (major, minor, and middle). Each probability expression from this network is evaluated to yield a linear function of the parameters in the probability model. By this approach the constraints specified as premises translate into linear equalities and inequalities involving a few real-valued variables. The problem's figure (schema) describes which specific probabilities are constrained, relative to those that are queried. Using linear optimization methods, the minimum and maximum feasible values of certain queried probabilities are computed, subject to the constraints given as premises. These computed solutions determine precisely which conclusions are necessary consequences of the premises. In this way, Aristotle's logical deductions can be accomplished by means of numerical computation., Comment: reorganized

We investigate the application of classification techniques to utility elicitation. In a decision problem, two sets of parameters must generally be elicited: the probabilities and the utilities. While the prior and conditional probabilities in the model do not change from user to user, the utility models do. Thus it is necessary to elicit a utility model separately for each new user. Elicitation is long and tedious, particularly if the outcome space is large and not decomposable. There are two common approaches to utility function elicitation. The first is to base the determination of the users utility function solely ON elicitation OF qualitative preferences.The second makes assumptions about the form AND decomposability OF the utility function.Here we take a different approach: we attempt TO identify the new USERs utility function based on classification relative to a database of previously collected utility functions. We do this by identifying clusters of utility functions that minimize an appropriate distance measure. Having identified the clusters, we develop a classification scheme that requires many fewer and simpler assessments than full utility elicitation and is more robust than utility elicitation based solely on preferences. We have tested our algorithm on a small database of utility functions in a prenatal diagnosis domain and the results are quite promising., Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998)

This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization problem into a pair of mixed binary-linear programs. The solutions to these two integer-linear reformulations provide upper and lower bounds on the global solution to the original polynomial program. The tightness of these bounds, the error in approximating each polynomial expression, and the number of constraints that must be added in the process of reformulation all depend on the error tolerance specified by the user for each variable in the original polynomial program. As these error tolerances approach zero the size of the reformulated programs increases and the calculated interval bounds converge to the true global solution., Comment: 18 pages

The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the probabilities of logical propositions. An alternative direct probability encoding scheme is presented, which allows statements of implication and quantification to be modeled directly as constraints on conditional probabilities. Several example problems are solved, from Johnson-Laird's aces to Smullyan's zombies. Many apparently challenging problems in logic turn out to be simple problems in algebra and computer science: systems of polynomial equations or linear optimization problems. This work extends the mathematical logic and parametric probability methods invented by George Boole., Comment: 39 pages including 4 page appendix; new title, additional clarifications, correction of bugs introduced into one example in the last revision

A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms is computed from the solution to the corresponding system of polynomial equations. A reference by a formula to its own provability is shown to be a recurrence relation, which can be either interpreted as such to generate a discrete dynamical system, or interpreted in a static way to create an additional simultaneous equation. In this framework the truth values of logical formulas and other polynomial objectives have complex data structures: sets of elementary values, or dynamical systems that generate sets of infinite sequences of such solution-value sets. Besides the routine result that a formula has a definite elementary value, these data structures encode several exceptions: formulas that are ambiguous, unsatisfiable, unsteady, or contingent. These exceptions represent several semantically different types of undecidability; none causes any fundamental problem for mathematics. It is simple to calculate that Goedel's formula, which asserts that it cannot be proven, is exceptional in specific ways: interpreted statically, the formula defines an inconsistent system of equations (thus it is called unsatisfiable); interpreted dynamically, it defines a dynamical system that has a periodic orbit and no fixed point (thus it is called unsteady). These exceptions are not catastrophic failures of logic; they are accurate mathematical descriptions of Goedel's self-referential construction. Goedel's analysis does not reveal any essential incompleteness in formal reasoning systems, nor any barrier to proving the consistency of such systems by ordinary mathematical means., Comment: 45 pages; revised to clarify some general notation and specific points on polynomials, remove extraneous material, fix typos, and introduce the Pythagorean fallacy

This paper describes the use of undergraduate teaching and research assistants in the Psychology Department of a university. This program creates additional resources for the department and provides mentoring opportunities for students who are interested in going to graduate school. Hiring and training undergraduates to be teaching assistants is cost effective as the number of students in each class section can be increased without needing additional adjunct faculty. Students interested in becoming teaching assistants must take a course titled "Psychology Applied to Teaching" before their placement. They are then mentored by individual faculty members. A student who has been a teaching assistant for at least one semester becomes the Head Teaching Assistant to work with the new assistants and to do some of the mentoring as well. The research assistant program relies on individual faculty members who are encouraged to involve undergraduates in their research. A list of some publications with which student teaching and research assistants have been associated is attached. (SLD)