Deduction Systems (Texts in Computer Science)

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Perhaps using this notation for "equivalent by definition" would be better than bi-directional implication in some ways, though it's not much better for visual pattern matching:. The point is not just to render the notes nicely but to capture the knowledge in a way I and my collaborators can exploit by machine. The dialect imposes very little in the way of logical constraints over and above the way articles are typically written:. I tried to figure out how it works from the python source code but quickly got lost.

While attempting a scala port pfmorris to sort out the latent types, I realized the python source wasn't the best explanation of what's going on. The common notions file explain the use of Morris Logic with second-order schemators and Hilbert's epsilon for indefinite description. Working on the scala port got sufficiently repetetive and tedious that I wondered if automating it might work better.

The byproduct is py2scala , which turns out to be more directly useful for python refactoring than porting. More on that in another episode, I hope. The notation I used for formal proofs throughout my time at U. Austin, and to this day for similar tasks, comes from the Philosophy K: Logic, Sets and Functions course. The instructors were Kant and Bonevac.

I remember Kant giving most of the lectures, but Bonevac wrote the text :. The idea of an axiomatic system is old, dating at least from the time of Euclid. The Stoics, who were Greek philosophers of the third century B. In contrast, natural deduction systems are relatively new; Gerhard Gentzen, a German logician, and Stanislaw Jaskowski, a Polish student of Jan Lukasiewicz, independently proposed the first natural deduction systems in The system of this book owes a great deal, as well, to innovations by the American logicians Willard van Orman Quine, Frederic B.

Fitch, Donald Kalish and Richard Montague. The history was lost on me at the time, but it took on practical relevance as I looked at metamath. I could read the proofs fairly well, but when I tried to write even a simple one, I was stuck. It wasn't until I discovered a natural deduction based metamath system that I realized the conventional metamath proofs are written Hilbert-style and the system I learned is a natural deduction system, and converting Hilbert-style to natural deduction is notoriously difficult.

The modern rendition of the text seems to be a more polished book, Deduction. Consider, for example, the process for deciding how to approach a destination in a hostile environment. The decision-makers may have access to tremendous amounts of heterogeneous information, though not all of it available predictably. Some information is collected over the longer term, such as knowledge about roads and bridges, inferred social networks, patterns of individuals and organizations, social schedules market days and hours, religious services, regular meetings , the attitudes of nearby populations, and general environmental conditions.

Along with that, near-term information is gathered about particular threats, weather and wind conditions, influxes or outflows of population e. Each of these sources has its own uncertainties, and the quality and variability of the sources may be interdependent: for instance, the attitudes of surrounding populations can change depending on what information is communicated day by day, and by the positioning of troops.

Decision making for some processes, such as a multi-day approach to a new location, might unfold through a number of smaller-scale decisions; whereas decision-making in some other cases, such as whether or not to order a drone strike, is a single yes-no decision with high consequences. Other military decision making can be even more complex. Consider, planning for a major deployment. The multi-month needs of the force must be anticipated, supply chains established, logistics planned, and so on. These demands have existed for centuries, and since at least World War II a strong foundation of analytical tools has been developed.

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As an operation unfolds, it will build on reports and forecasts about weather, tide, wind, and storm conditions, movements of others on transportation routes, aerial images and other sensed data, human-generated reports from the field, media and intelligence reports, information traffic over social media, data exhaust, and so on. This broad range of information strains the capabilities of the tools and of the planners to. A well-known example is the use of misspellings gathered during previous searches to improve the front-end interpreter used by search engines.

At the same time, the relative ease with which inputs can be assembled has opened the door to compressing the decision making timeline, which further challenges the human planners. Decision making of similar complexity occurs in many other contexts. Teams that manage the response to major disasters, such as damage from Hurricane Sandy in the United States or from the Fukushima Daiichi nuclear accident in Japan, must incorporate a very broad range of information from multiple heterogeneous sources—e.

The response to the Boston Marathon bombing is another case, one that may be more akin to some military decision making. In addition to multiple, partial information, the decision makers who managed the immediate response had to incorporate preliminary forensic evidence, crowd sourced inputs of untested value , and other inputs, all with a great deal of time pressure. The decisions constituted a family of choices, such as where to deploy police, which areas to consider high risk for citizens and police, top-priority search areas, the best information to follow or expand, and how to conduct the search.

In all of these cases, the decision making is a team effort, with many experts evaluating information and using their analysis and judgment to create portions of the overall decision or plan. Overlain on that is a process by which team members challenge one another and jointly merge their individual insights to create a bigger picture.

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Ultimate decisions are made by team leaders based on this funneling of information and analysis. It is difficult for humans to make good decisions in such complex situations. It must be remembered that the ultimate goal is to make good decisions: merely finding a way to analyze and incorporate all the data is not valuable unless it also leads more reliably to good decisions.

Computational support in the form of large-scale data collection and analysis, visualization, etc. For example, computation is in the control processes for all manner of processing plants chemical processing, nuclear power generation and petroleum refining , infrastructure electric grid and telecommunications , manufacturing chip fabrication and large scale baking plants , assembly electronics and automotive robotic assembly , transactions credit card and banking and the military management of theater operations.

The rest of this chapter focuses on the three components of such complex decision-making: the essence of decision making; exploiting the vast amounts of data that have become available as the basis for complex decision making; and the nature of collaboration that is possible between humans and machines in the process of making complex decisions. The committee chose not to address whether, and if so how, autonomous systems might someday replace humans as decision makers in complex situations.

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Decision making is integral to the human experience. Our ability to consider the implications of future actions, ponder cause and effect, and leverage our exquisite executive function capabilities sets us apart from the rest of the animal kingdom. Yet our decision making. In addition, some decisions must be made against near time constraints.

A decision not to act or a failure to decide at all is a decision in some dynamic, rapidly-changing environments. In addition to reaching a decision about a course of action, one also must make decisions about which information to consider out of the vast amounts that are available, weighing the cost of obtaining the information against its potential value. Such decisions about process can affect the quality of the ultimate decision, and they may be challenging in many of the same ways because of the multitude of options available.

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Decision making tends to be context dependent; it often requires understanding of not only the observed or experienced situation but also of the relevant history and background. Early theories of decision making focused upon serial processing models, where sensor processes fed perception and the several memory systems under study working, or short-term, memory, and long-term memory in a relatively straightforward process.

Decision making itself was presumed to be a logical deduction from the information provided, and these models were often described in the language of traditional information technology and processing. Thus, the widely cited OODA-loop model originated by John Boyd has a series of primarily sequential stages: Observation, Orientation analysis , Decision, and Action with feedback from the stages of decision and action as well as from the environment back to the orientation stage. Although a useful paradigm for training—it was designed for situations requiring a rapid response time, such as decision making by fighter pilots, so it is necessarily simplified—it is a coarse model for studying the frontiers of decision making it oversimplifies the underlying processes.

As a result, although widely referred to in operational situations and for training, it is not a common framework in the research community. Recently the military literature has addressed the inadequacy of the OODA loop to deal with complex situations where the decision maker does not have access to a model of the underlying mechanisms between actions and outcomes Benson and Rotkoff, A red team could identify ways in which observations might be made misleading, decisions anticipated, and actions countered, thus undercutting the applicability of an OODA-loop description of the decision-making process.

In addition, the implied sequential nature of the OODA loop—even if there is feedback between stages and perhaps multiple trips through the loop—does not fit well with real, complex decision making. In responding to a natural disaster, for example, decision making is extremely interactive, which is not modeled well with an OODA framework. Both of these exercises. The committee believes that the OODA-loop construct is not well matched to complex decision making with large volumes of information; while the four stages are part of any decision-making process, they can be combined in multiple ways.

Consequently, it developed the following finding:. Finding 1. A common representation of the decision-making process, used to train fighter pilots in rapid decision-making for air combat, calls for sequential steps to observe, update beliefs, choose an action, and take the action the so-called OODA loop. While those steps are inherent to any careful decision making, for complex decisions the OODA loop framework does not readily reflect feedback loops between the steps and branching to consider multiple choices of action, both of which are common.

The study of decision making in complex situations, and the design of automated decision support systems, requires an understanding of those complexities. Thus the OODA-loop framework may not be sufficient in these contexts. Early decision-making models tended to assume that decision making occurred at the conscious level of processing.


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A more nuanced view was presented by the theorist, J. Rasmussen , who divided the decision-making process of skilled operators into three categories: Skill-, Rule-, and Knowledge-based procedures.


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  • Skill-based behavior refers to those capabilities that are sensory-motor and developed after a period of training, such as riding a bike. Rule-based behavior refers to those that are based on learned rules or procedures, such as following a recipe. In this taxonomy, knowledge-based processing is the highest level of cognitive control because it includes the challenge of solving novel problems Cummings, For example, recent evidence about human thought implies that decisions by experts are often reached subconsciously, with reason and logic coming afterward to justify the decision Mercier and Sperber, Recognition-primed decision making Klein, involves rapid pattern matching to the situation, one of the powerful properties of fast, subconscious systems.

    Heuristics and rule-following present a mix of behavior at the conscious and subconscious levels of processing. At the subconscious level, researchers have identified numerous heuristics that people use to simplify and speed up decision making—effectively, pattern matching to situations previously experienced. This decision making is often referred to as fast and frugal Gigerenzer and Goldstein, The past decade has seen significant progress in developing technologies and methods that support human sense-making and decision-making processes in complex domains. Understanding the dynamics of a complex system or organization can help one foresee the side effects of a decision or anticipate events before they occur.

    Many studies have been undertaken on measuring and supporting situation awareness, especially for individual decision makers, but there are still major gaps in our understanding of how to design and evaluate technologies and methods to provide effective cognitive support for individual and team sense making Klein et al.

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    Traditional models of human decision making focus entirely upon mental processing—all the action takes place in the brain—but another important trend in our understanding of human behavior is to understand the role of embodiment—that the human body exists in the world, interacting with it in ways that enhance our ability to function.

    Norman described it as a melding of knowledge in the head and knowledge in the world, because when accomplishing some task, the environment provides much of the information required as well as providing constraints, guides, and suggested courses of action Norman, , Information systems can be designed to support the human decision maker in tasks or subtasks that are domain or situation specific.

    More and more systems are able to respond intelligently to queries in natural language e. At the same time, some of these technologies have also complicated the decision-making process. For example, social networking was responsible for many false claims just after the Boston Marathon bombing in April , and subsequently, throughout the hunt for the perpetrators. In addition to meeting the challenge of supporting its intended user, systems that incorporate data analysis can encounter situations in which hostile entities intend to deceive the decision maker.

    When such strategic actors are present, they might play a meta-level role in determining what we are able to observe. These potential vulnerabilities must be considered when designing and using information systems as decision aids. For example, our actions, including further information gathering, can inform adversaries about our current state of knowledge.

    Last accessed March 19, A decision-making context and process can be characterized along dimensions such as the following:. The list above characterizes many aspects of the human decision-making process, and each dimension will influence an information system that is designed to support decision making. Any or all of these dimensions might be considered when developing such an information system. Many other factors have crucial effects on decisionmaking, such as emotions, social context, relationships, organizational structures, authority systems, and so forth.