The “grand problem” of AI has always been to build artificial agents with human-like intelligence. That is the stuff of science fiction, but it is also the ultimate aspiration of AI. In retrospect, we can understand what a difficult problem this is, so since its inception AI has focused more on small manageable problems, with the hope that progress there will have useful implications for the grand problem. Now there is a resurgence of interest in tackling the grand problem head-on. (...) Perhaps AI has made enough progress on the little problems that we can fruitfully address the big problem. The objective is to build agents of human-level intelligence capable of operating in environments of real-world complexity. I will refer to these as GIAs — “generally intelligent agents”. OSCAR is a cognitive architecture for GIAs, implemented in LISP.1 OSCAR draws heavily on my work in philosophy concerning both epistemology (Pollock 1974, 1986, 1990, 1995, 1998, 2008b, 2008; Pollock and Cruz 1999; Pollock and Oved, 2005) and rational decision making (2005, 2006, 2006a). (shrink)
Pollock describes an exciting theory of rationality and its partial implementation in OSCAR, a computer system whose descendants will literally be persons.
"A sequel to Pollock's How to Build a Person, this volume builds upon that theoretical groundwork for the implementation of rationality through artificial ...
In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their ...
Pollock argues that theories of ideal rationality are largely irrelevant to the decision making of real agents. Thinking about Acting aims to provide a theory of "real rationality.".
Contingencies of the early nuclear arms race Content Type Journal Article Pages 1-23 DOI 10.1007/s11016-010-9495-z Authors S. S. Schweber, Department of the History of Science, Harvard University, Science Center 371, Cambridge, MA 02138, USA Alex Wellerstein, Department of the History of Science, Harvard University, Science Center 371, Cambridge, MA 02138, USA Ethan Pollock, Department of History, Box N, Brown University, Providence, RI 02912, USA Barton J. Bernstein, History Department, Building 200, Stanford University, Stanford, CA 94305-2024, USA Michael D. (...) Gordin, History Department, 305 Dickinson Hall, Princeton University, Princeton, NJ 08544, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796. (shrink)
In a previous paper by Pollock and Singh, it was proven that the total entropy of de Sitter space-time is equal to zero in the spatially flat case K=0. This result derives from the fundamental property of classical thermodynamics that temperature and volume are not necessarily independent variables in curved space-time, and can be shown to hold for all three spatial curvatures K=0,±1. Here, we extend this approach to Schwarzschild space-time, by constructing a non-vacuum interior space with line element (...) ds 2=e2λ(r) dt 2−e−2λ(r) dr 2−r 2(dθ 2+sin2 θdϕ 2), where $\mathrm{e}^{2{\lambda }(r)}=-\frac{1}{2}(1-\frac{r^{2}}{R_{0}^{2}})$ , which matches onto the vacuum exterior Schwarzschild metric in such a way that e2λ and d(e2λ )/dr are both continuous at the Schwarzschild radius R 0=2M. Then we show that the volume entropy is equal to A/4, where $A\equiv 4\pi R_{0}^{2}$ is the area of the apparent horizon, as found by Hawking. (shrink)
In the past, few mainstream epistemologists have endorsed Bayesian epistemology, feeling that it fails to capture the complex structure of epistemic cognition. The defenders of Bayesian epistemology have tended to be probability theorists rather than epistemologists, and I have always suspected they were more attracted by its mathematical elegance than its epistemological realism. But recently Bayesian epistemology has gained a following among younger mainstream epistemologists. I think it is time to rehearse some of the simpler but still quite devastating objections (...) to Bayesian epistemology. Most of these objections are familiar, but have never been adequately addressed by the Bayesians. (shrink)
Human beings think of themselves in terms of a privileged non-descriptive designator — a mental “I”. Such thoughts are called “_de se_” thoughts. The mind/body problem is the problem of deciding what kind of thing I am, and it can be regarded as arising from the fact that we think of ourselves non-descriptively. Why do we think of ourselves in this way? We investigate the functional role of “I” (and also “here” and “now”) in cognition, arguing that the use of (...) such non-descriptive “reflexive” designators is essential for making sophisticated cognition work in a general-purpose cognitive agent. If we were to build a robot capable of similar cognitive tasks as humans, it would have to be equipped with such designators. (shrink)
Internalism in epistemology is the view that all the factors relevant to the justification of a belief are importantly internal to the believer, while externalism is the view that at least some of those factors are external. This extremely modest first approximation cries out for refinement (which we undertake below), but is enough to orient us in the right direction, namely that the debate between internalism and externalism is bound up with the controversy over the correct account of the distinction (...) between justified beliefs and unjustified beliefs.1 Understanding that distinction has occasionally been obscured by attention to the analysis of knowledge and to the Gettier problem, but our view is that these problems, while interesting, should not completely seduce philosophers away from central questions about epistemic justification. A plausible starting point in the discussion of justification is that the distinction between justified beliefs and unjustified beliefs is not the same as the distinction between true beliefs and false beliefs. This follows from the mundane observation that it is possible to rationally believe.. (shrink)
The strategy of this paper is to throw light on rational cognition and epistemic justification by examining irrationality. Epistemic irrationality is possible because we are reflexive cognizers, able to reason about and redirect some aspects of our own cognition. One consequence of this is that one cannot give a theory of epistemic rationality or epistemic justification without simultaneously giving a theory of practical rationality. A further consequence is that practical irrationality can affect our epistemic cognition. I argue that practical irrationality (...) derives from a general difficulty we have in overriding built-in shortcut modules aimed at making cognition more efficient, and all epistemic irrationality can be traced to this same source. A consequence of this account is that a theory of rationality is a descriptive theory, describing contingent features of a cognitive architecture, and it forms the core of a general theory of “voluntary” cognition — those aspects of cognition that are under voluntary control. It also follows that most of the so-called “rules for rationality” that philosophers have proposed are really just rules describing default (non- reflexive) cognition. It can be perfectly rational for a reflexive cognizer to break these rules. The “normativity” of rationality is a reflection of a built-in feature of reflexive cognition — when we detect violations of rationality, we have a tendency to desire to correct them. This is just another part of the descriptive theory of rationality. Although theories of rationality are descriptive, the structure of reflexive cognition gives philosophers, as human cognizers, privileged access to certain aspects of rational cognition. Philosophical theories of rationality are really scientific theories, based on inference to the best explanation, that take contingent introspective data as the evidence to be explained. (shrink)
When your word processor or email program is running on your computer, this creates a "virtual machine” that manipulates windows, files, text, etc. What is this virtual machine, and what are the virtual objects it manipulates? Many standard arguments in the philosophy of mind have exact analogues for virtual machines and virtual objects, but we do not want to draw the wild metaphysical conclusions that have sometimes tempted philosophers in the philosophy of mind. A computer file is not made of (...) epiphenomenal ectoplasm. I argue instead that virtual objects are "supervenient objects". The stereotypical example of supervenient objects is the statue and the lump of clay. To this end I propose a theory of supervenient objects. Then I turn to persons and mental states. I argue that my mental states are virtual states of a cognitive virtual machine implemented on my body, and a person is a supervenient object supervening on his cognitive virtual machine. (shrink)
This is a text for an introductory symbolic logic course. It is based upon an old text that I wrote in 1969, which is long out of print. But it modifies the approach of that book to reflect theoretical work that I have done on theorem proving in the..
Postulational approaches attempt to understand the dynamics of belief revision by appealing to no more than the set of beliefs held by an agent and the logical relations between them. It is argued there that such an approach cannot work. A proper account of belief revision must also appeal to the arguments supporting beliefs, and recognize that those arguments can be defeasible. If we begin with a mature epistemological theory that accommodates this, it can be seen that the belief revision (...) operators on which the postulational theories are based are ill-defined. It is further argued that there is no way to repair the definitions so as to retain the spirit of those theory. Belief revision is better studied from within an independently motivated epistemological theory. (shrink)
There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.
Imagine yourself sitting on your front porch, sipping your morning coffee and admiring the scene before you. You see trees, houses, people, automobiles; you see a cat running across the road, and a bee buzzing among the flowers. You see that the flowers are yellow, and blowing in the wind. You see that the people are moving about, many of them on bicycles. You see that the houses are painted different colors, mostly earth tones, and most are one-story but a (...) few are two-story. It is a beautiful morning. Thus the world interfaces with your mind through your senses. There is a strong intuition that we are not disconnected from the world. We and the other things we see around us are part of a continuous whole, and we have direct access to them through vision, touch, etc. However, the philosophical tradition tries to drive a wedge between us and the world by insisting that the information we get from perception is the result of inference from indirect evidence that is about how things look and feel to us. The philosophical problem of perception is then to explain what justifies these inferences. We will focus on visual perception. Figure one presents a crude diagram of the cognitive system of an agent capable of forming beliefs on the basis of visual perception. Cognition begins with the stimulation of the rods and cones on the retina. From that physical input, some kind of visual processing produces an introspectible visual image. In response to the production of the visual image, the cognizer forms beliefs about his or her surroundings. Some beliefs the perceptual beliefs are formed as direct responses to the visual input, and other beliefs are inferred from the perceptual beliefs. The perceptual beliefs are, at the very least, caused or causally influenced by having the image. This is signified by the dashed arrow marked with a large question mark. We will refer to this as the mystery link. Figure one makes it apparent that in order to fully understand how knowledge is based on perception, we need three different theories.. (shrink)
Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple (...) and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills. (shrink)
In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.
An argument is self-defeating when it contains defeaters for some of its own defeasible lines. It is shown that the obvious rules for defeat among arguments do not handle self-defeating arguments correctly. It turns out that they constitute a pervasive phenomenon that threatens to cripple defeasible reasoning, leading to almost all defeasible reasoning being defeated by unexpected interactions with self-defeating arguments. This leads to some important changes in the general theory of defeasible reasoning.
Since Gettier, much of epistemology has focused on analyzing “S knows that P”, but that is not my interest. My general interest is in rational cognition — both in what it is to be rational, and in how rational cognition works. The traditional epistemological question, “How do you know?”, can be taken as addressing part of the more general problem of producing a theory of rational cognition. It is about specifically epistemic rationality. I interpret this question literally, as a question (...) about how we should proceed in our epistemic endeavors. Epistemological theories that try to answer this question are theories of procedural epistemology (see my 1998), and when, from this perspective, we assess beliefs in terms of their justifiedness, the concept of justification is one of procedural epistemic justification. Whether this has anything to do with the analysis of knowledge is an open question, and not one that I have much interest in addressing. (shrink)
It’s morning. You sit down at your desk, cup of coffee in hand, and prepare to begin your day. First, you turn on your computer. Once it is running, you check your e-mail. Having decided it is all spam, you trash it. You close the window on your e-mail program, but leave the program running so that it will periodically check the mail server to see whether you have new mail. If it finds new mail it will alert you by (...) playing a musical tone. Next you start your word processor. You have in mind to write a paper in moral philosophy about whether people who send spam. (shrink)
The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)
The “grand problem” of AI has always been to build artificial agents of human-level intelligence, capable of operating in environments of real-world complexity. OSCAR is a cognitive architecture for such agents, implemented in LISP. OSCAR is based on my extensive work in philosophy concerning both epistemology and rational decision making. This paper provides a detailed overview of OSCAR. The main conclusions are that such agents must be capablew of operating against a background of pervasive ignorance, because the real world is (...) too complex for them to know more than a small fraction of what is true. This is handled by giving the agent the power to reason defeasibily. The OSCAR system of defeasible reasoning is sketched. It is argued that if epistemic cognition must be defeasible, planning must also be done defeasibly, and the best way to do that is to reason defeasibly about plans. A sketch is given about how this might work. (shrink)
In a number of recent papers I have been developing the theory of "nomic probability," which is supposed to be the kind of probability involved in statistical laws of nature. One of the main principles of this theory is an acceptance rule explicitly designed to handle the lottery paradox. This paper shows that the rule can also handle the paradox of the preface. The solution proceeds in part by pointing out a surprising connection between the paradox of the preface and (...) the gambler's fallacy. (shrink)
The objective of this paper is to construct an implementable theory of rational decision-making for cognitive agents subject to realistic resource constraints. It is argued that decision-making should select actions indirectly by selecting plans that prescribe them. It is also argued that although expected values provide the tool for evaluating plans, plans cannot be compared straightforwardly in terms of their expected values, and the objective of a realistic agent cannot be to find optimal plans. The theory of Locally Global planning (...) is proposed as a realistic alternative to standard "maximizing" theories of rational decision-making. (shrink)
This article sketches a theory of objective probability focusing on "nomic probability", which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the "statistical syllogism". It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)
The objective of this book is to produce a theory of rational decision making for realistically resource-bounded agents. My interest is not in “What should I do if I were an ideal agent?”, but rather, “What should I do given that I am who I am, with all my actual cognitive limitations?” The book has three parts. Part One addresses the question of where the values come from that agents use in rational decision making. The most comon view among philosophers (...) is that they are based on preferences, but I argue that this is computationally impossible. I propose an alternative theory somewhat reminiscent of Bentham, and explore how human beings actually arrive at values and how they use them in decision making. Part Two investigates the knowledge of probability that is required for decision-theoretic reasoning. I argue that subjective probability makes no sense as applied to realistic agents. I sketch a theory of objective probability to put in its place. Then I use that to define a variety of causal probability and argue that this is the kind of probability presupposed by rational decision making. So what is to be defended is a variety of causal decision theory. Part Three explores how these values and probabilities are to be used in decision making. In chapter eight, it is argued first that actions cannot be evaluated in terms of their expected values as ordinarily defined, because that does not take account of the fact that a cognizer may be unable to perform an action, and may even be unable to try to perform it. An alternative notion of “expected utility” is defined to be used in place of expected values. In chapternine it is argued that individual actions cannot be the proper objects of decision-theoretic evaluation. We must instead choose plans, and select actions indirectly on the grounds that they are prescribed by the plans we adopt. However, our objective cannot be to find plans with maximal expected utilities. Plans cannot be meaningfully compared in that way.. (shrink)
Bayesians take “definite” or “single-case” probabilities to be basic. Definite probabilities attach to closed formulas or propositions. We write them here using small caps: PROB(P) and PROB(P/Q). Most objective probability theories begin instead with “indefinite” or “general” probabilities (sometimes called “statistical probabilities”). Indefinite probabilities attach to open formulas or propositions. We write indefinite probabilities using lower case “prob” and free variables: prob(Bx/Ax). The indefinite probability of an A being a B is not about any particular A, but rather about the (...) property of being an A. In this respect, its logical form is the same as that of relative frequencies. For instance, we might talk about the probability of a human baby being female. That probability is about human babies in general — not about individuals. If we examine a baby and determine conclusively that she is female, then the definite probability of her being female is 1, but that does not alter the indefinite probability of human babies in general being female. Most objective approaches to probability tie probabilities to relative frequencies in some way, and the resulting probabilities have the same logical form as the relative frequencies. That is, they are indefinite probabilities. The simplest theories identify indefinite probabilities with relative frequencies.3 It is often objected that such “finite frequency theories” are inadequate because our probability judgments often diverge from relative frequencies. For example, we can talk about a coin being fair (and so the indefinite probability of a flip landing heads is 0.5) even when it is flipped only once and then destroyed (in which case the relative frequency is either 1 or 0). For understanding such indefinite probabilities, it has been suggested that we need a notion of probability that talks about possible instances of properties as well as actual instances.. (shrink)
Human beings think of themselves in terms of a privileged non-descriptive designator — a mental “I”. Such thoughts are called “de se” thoughts. The mind/body problem is the problem of deciding what kind of thing I am, and it can be regarded as arising from the fact that we think of ourselves non-descriptively. Why do we think of ourselves in this way? We investigate the functional role of “I” (and also “here” and “now”) in cognition, arguing that the use of (...) such non-descriptive “reflexive” designators is essential for making sophisticated cognition work in a general-purpose cognitive agent. If we were to build a robot capable of similar cognitive tasks as humans, it would have to be equipped with such designators. Once we understand the functional role of reflexive designators in cognition, we will see that to make cognition work properly, an agent must use a de se designator in specific ways in its reasoning. Rather simple arguments based upon how “I” works in reasoning lead to the conclusion that it cannot designate the body or part of the body. If it designates anything, it must be something non-physical. However, for the purpose of making the reasoning work correctly, it makes no difference whether “I” actually designates anything. If we were to build a robot that more or less duplicated human cognition, we would not have to equip it with anything for “I” to designate, and general physicalist inclinations suggest that there would be nothing for “I” to designate in the robot. In particular, it cannot designate the physical contraption. So the robot would believe “I exist”, but it would be wrong. Why should we think we are any different? (shrink)
When combining information from multiple sources and attempting to estimate the probability of a conclusion, we often find ourselves in the position of knowing the probability of the conclusion conditional on each of the individual sources, but we have no direct information about the probability of the conclusion conditional on the combination of sources. The probability calculus provides no way of computing such joint probabilities. This paper introduces a new way of combining probabilistic information to estimate joint probabilities. It is (...) shown that on a particular conception of objective probabilities, clear sense can be made of second-order probabilities (probabilities of probabilities), and these can be related to combinatorial theorems about proportions in finite sets as the sizes of the sets go to infinity. There is a rich mathematical theory consisting of such theorems, and the theorems generate corresponding theorems about secondorder probabilities. Among the latter are a number of theorems to the effect that certain inferences from probabilities to probabilities, although not licensed by the probability calculus, have probability 1 of producing correct results. This does not mean that they will always produce correct results, but the set of cases in which the inferences go wrong form a set of measure 0. Among these inferences are some enabling us to reasonably estimate the values of joint probabilities in a wide range of cases. A function called the Y-function is defined. The central theorem is the Y-Theorem, which tells us that if we know the individual probabilities for the different information sources and estimate the joint probability using the Y-function, the second-order probability of getting the right answer is 1. This mathematical result is tested empirically using a simple multi-sensor example. The Y-theorem agrees with Dempster's rule of combination in special cases, but not in general. (shrink)
This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)
Examples growing out of the Newcomb problem have convinced many people that decision theory should proceed in terms of some kind of causal probability. I endorse this view and define and investigate a variety of causal probability. My definition is related to Skyrms' definition, but proceeds in terms of objective probabilities rather than subjective probabilities and avoids taking causal dependence as a primitive concept.
This new edition of the classic Contemporary Theories of Knowledge has been significantly updated to include analyses of the recent literature in epistemology.
As a high school student, I rediscovered Hume’s problem of induction on my own. For a while, I was horrified. I thought, “We cannot know anything!” After a couple of weeks I calmed down and reasoned that there had to be something wrong with my thinking, and that led me quickly to the realization that good reasons need not be deductive, and to the discovery of defeasible reasoning. From there it was a short jump to a more general interest in (...) how rational cognition works. I am interested in rational cognition in general. Epistemology is one constituent of rational cognition, practical cognition (rational decision making) another. Much of the work on rational cognition begins with the supposition that only ideal agents can be truly rational. Real agents have limited powers of reasoning and limited memory capacity. It is often supposed that such resource-bounded agents can only approximate rationality, and that as philosophers we should confine our attention to ideal agents. If one wishes, one can of course define “rationality” in this way, but this has never been what interested me. We come to philosophy wondering what we should believe, what we should do, and how we should go about deciding these matters. These are questions about ourselves, with all of our cognitive limitations. For example, it is often claimed that ideal agents, with unlimited cognitive powers, should believe all of the logical consequences of their beliefs. But we, as real resource-bounded agents, cannot do that, so that is not something we should do. What I want to know is how I, as a real agent, should go about deciding what to believe and what to do. Thus my topic is real rationality as opposed to ideal rationality. In the realm of practical decision making, I have explored this distinction at great length in my recent book (2006). Here I will focus on its implications for epistemology. For many years epistemology was derailed by the Gettier problem.. (shrink)
Probability plays an essential role in many branches of AI, where it is typically assumed that we have a complete probability distribution when addressing a problem. But this is unrealistic for problems of real-world complexity. Statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&R), and (...) we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus for prob(P/Q&R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability — nomic probability — there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r,s:a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r,s:a).. (shrink)
The objective of the OSCAR Project is twofold. On the one hand, it is to construct a general theory of rational cognition. On the other hand, it is to construct an artificial rational agent (an "artilect") implementing that theory. This is a joint project in philosophy and AI.
One of the most striking characteristics of human beings is their ability to function successfully in complex environments about which they know very little. In light of our pervasive ignorance, we cannot get around in the world just reasoning deductively from our prior beliefs together with new perceptual input. As our conclusions are not guaranteed to be true, we must countenance the possibility that new information will lead us to change our minds, withdrawing previously adopted beliefs. In this sense, our (...) reasoning is “defeasible”. The question arises how defeasible reasoning works, or ought to work. In particular we need rules governing what a cognizer ought to believe given a set of interacting arguments some of which defeat others. That is what is called a “semantics” for defeasible reasoning, and this chapter will propose a new semantics that avoids certain clear counter-examples to all existing semantics. (shrink)
THE NATURE OF JURISPRUDENCE CONSIDERED IN RELATION TO SOME RECENT CONTRIBUTIONS TO LEGAL SCIENCE. Professor Holland of Oxford is to be congratulated on ...
Agents are entities that act upon the world. Rational agents are those that do so in an intelligent fashion. What is essential to such an agent is the ability to select and perform actions. Actions are selected by planning, and performing such actions is a matter of plan execution. So the essence of a rational agent is the ability to make and execute plans. This constitutes practical cognition. In order to perform its principal function of practical cognition, a rational agent (...) must also be able to acquire the knowledge of the world that is required for making and executing plans. This is done by epistemic cognition. Rational agents embedded in a realistically complicated world (e.g., human beings) may devote more time to epistemic cognition than to practical cognition, but even for such agents, epistemic cognition is in an important sense subservient to practical cognition. (shrink)
Counterexamples are constructed for the theory of rational choice that results from a direct application of classical decision theory to ordinary actions. These counterexamples turn on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. An alternative theory of rational choice is proposed that evaluates actions using a more complex measure, and then it is shown that this is equivalent to applying classical decision theory to "conditional (...) policies" rather than ordinary actions. (shrink)
New results in the theory of nomic probability have led to a theory of probable probabilities, which licenses defeasible inferences between probabilities that are not validated by the probability calculus. Among these are classical principles of direct inference together with some new more general principles that greatly strengthen direct inference and make it much more useful.
Counterexamples are constructed for classical decision theory, turning on the fact that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that there is no way to define optimality for plans that makes the finding of optimal plans the desideratum of rational decision-making. An alternative called “locally global planning” is proposed as a replacement for classical decision theory. Decision-making becomes a non-terminating process without a precise target rather than (...) a terminating search for an optimal solution. (shrink)
In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus (...) for prob(P/Q&R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability — nomic probability — there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r,s,a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r,s,a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities.. (shrink)
Decision-theoretic planning is normally based on the assumption that plans can be compared by comparing their expected-values, and the objective is to find an optimal plan. This is typically defended by reference to classical decision theory. However, classical decision theory is actually incompatible with this “simple plan-based decision theory”. A defense of plan-based decision theory must begin by showing that classical decision theory is incorrect insofar as the two theories conflict, so this paper begins by raising objections to classical decision (...) theory . First, there is a discussion of the considerations arising out of the Newcomb problem that have given rise to causal decision theory. Next, counterexamples are constructed for classical decision theory turning on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. A proposal is made for how to repair classical decision theory in light of these counterexamples. But then turning to the concept of an “alternative” that is presupposed by classical decision theory, it is argued that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that optimality cannot be defined for plans, and even if it could be, it would not be reasonable to require rational agents to find optimal plans. So simple plan-based decision theory must also be rejected. An alternative called “locally global planning” is proposed as a replacement for both classical decision theory and simple plan-based decision theory. (shrink)
In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus (...) for prob(P/Q&R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability — nomic probability — there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r,s:a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r,s:a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities.. (shrink)
This article attempts to show that certain alternatives that have been proposed to the classical principle of induction are necessarily inferior to it. The simplest versions of these ?counter?inductionist? policies are logically inconsistent, and consistent formulations are less reliable than the straight principle of induction.
Cognitive agents form beliefs representing the world, evaluate the world as represented, form plans for making the world more to their liking, and perform actions executing the plans. Then the cycle repeats. This is the doxastic-conative loop, diagrammed in figure one.1 Both human beings and the autonomous rational agents envisaged in AI are cognitive agents in this sense. The cognition of a cognitive agent can be subdivided into two parts. Epistemic cognition is that kind of cognition responsible for producing and (...) maintaining beliefs. Practical cognition evaluates the world, adopts plans, and initiates action. There is a massive literature both in philosophy and artificial intelligence concerning various aspects of epistemic cognition, and large parts of it are well understood. Practical cognition is less well understood. We can usefully divide practical cognition into five parts: (1) the evaluation of the world as represented by the agent’s beliefs, (2) the adoption of goals for changing it, (3) the construction of plans for achieving goals, (4) the adoption of plans, and (5) the execution of plans. There is a substantial literature in AI concerning the construction and execution of plans, and I will say nothing further about those topics here. This paper will focus on the evaluative aspects of practical cognition. Evaluation plays an essential role in both goal selection and plan adoption. My concern here is the investigation of evaluation as a cognitive enterprise performed by cognitive agents. I am interested both in how it is performed in human beings and how it might be performed in artificial rational agents. (shrink)
A rational agent (artificial or otherwise) residing in a complex changing environment must gather information perceptually, update that information as the world changes, and combine that information with causal information to reason about the changing world. Using the system of defeasible reasoning that is incorporated into the OSCAR architecture for rational agents, a set of reasonschemas is proposed for enabling an agent to perform some of the requisite reasoning. Along the way, solutions are proposed for the Frame Problem, the Qualification (...) Problem, and the Ramification Problem. The principles and reasoning described have all been implemented in OSCAR. (shrink)
Stuart Russell [14] describes rational agents as --œthose that do the right thing--�. The problem of designing a rational agent then becomes the problem of figuring out what the right thing is. There are two approaches to the latter problem, depending upon the kind of agent we want to build. On the one hand, anthropomorphic agents are those that can help human beings rather directly in their intellectual endeavors. These endeavors consist of decision making and data processing. An agent that (...) can help humans in these enterprises must make decisions and draw conclusions that are rational by human standards of rationality. Anthropomorphic agents can be contrasted with goal-oriented agents --” those that can carry out certain narrowly-defined tasks in the world. Here the objective is to get the job done, and it makes little difference how the agent achieves its design goal. (shrink)
Direct inference derives values for definite (single-case) probabilities from those of related indefinite (general) probabilities. But direct inference is less useful than might be supposed, because we often have too much information, with the result that we can make conflicting direct inferences, and hence they all undergo collective defeat, leaving us without any conclusion to draw about the value of the definite probabilities. This paper presents reason for believing that there is a function — the Y- function — that can (...) be used to combine different indefinite probabilities to yield a single value for the definite probability. Thus we get a kind of “computational” direct inference. (shrink)
This paper is informed by my own participant observation and uses my own ethnography which included conducting in-depth interviews with anonymous paid egg donors and observing a listserv for women considering, pursuing, or having completed egg donation, to illustrate the way that power operates at this particular site of the reproductive center in postmodernity. After outlining who the consumers and providers of eggs are, I will use Foucault's concepts of biopower, disciplinary power, and normativity to describe how anonymous paid egg (...) donation plays a socially useful role in reproducing privilege and in preserving the myth of the nuclear family. Drawing on feminist theorizing to problematize altruism, I will show how the construction of the altruist narrative feeds the preservation of that myth by giving egg donors appropriately feminine motivations. Finally, I will focus on one particular site of resistance on the part of egg donorsâcontrolling their self-presentation, tweaking the pool of eggsâto underscore the simultaneity of control of and control by egg donors. (shrink)
This paper presents a challenge problem for decision-theoretic planners. State-space planners reason globally, building a map of the parts of the world relevant to the planning problem, and then attempt to distill a plan out of the map. A planning problem is constructed that humans find trivial, but no state-space planner can solve. Existing POCL planners cannot solve the problem either, but for a less fundamental reason.
This paper investigates decision-theoretic planning in sophisticated autonomous agents operating in environments of real-world complexity. An example might be a planetary rover exploring a largely unknown planet. It is argued th a t existing algorithms for decision-theoretic planning are based on a logically incorrect theory of rational decision making. Plans cannot be evaluated directly in terms of their expected values, because plans can be of different scopes, and they can interact with other previously adopted plans. Furthermore, in the real world, (...) the search for optimal plans is completely intractable. An alternative theory of rational decision making is proposed, called “locally global planning”. (shrink)
ACKNOWLEDGEMENTS I would like to thank my family and friends, without whose support, understanding, and love this study could probably not have been written ...
The aim of this paper is to investigate two related aspects of human reasoning, and use the results to construct an automated theorem prover for the predicate calculus that at least approximately models human reasoning. The result is a non-resolution theorem prover that does not use Skolemization. It involves two central ideas. One is the interest constraints that are of central importance in guiding human reasoning. The other is the notion of suppositional reasoning, wherein one makes a supposition, draws inferences (...) that depend upon that supposition, and then infers a conclusion that does not depend upon it. Suppositional reasoning is involved in the use of conditionals and reductio ad absurdum, and is central to human reasoning with quantifiers. The resulting theorem prover turns out to be surprisingly efficient, beating most resolution theorem provers on some hard problems. (shrink)
Most automated theorem provers are clausal-form provers based on variants of resolutionrefutation. In my [1990], I described the theorem prover OSCAR that was based instead on natural deduction. Some limited evidence was given suggesting that OSCAR was suprisingly efficient. The evidence consisted of a handful of problems for which published data was available describing the performance of other theorem provers. This evidence was suggestive, but based upon too meager a comparison to be conclusive. The question remained, “How does natural deduction (...) compare with resolution-refutation?” In the ensuing seven years, OSCAR has evolved in important ways, and other developments have made it possible to collect more accurate comparative data. Specifically, the creation of the TPTP library of problems for theorem provers,1 and the availability of important theorem provers on the world wide web, make objective comparisons easier. These developments recently inspired Geoff Sutcliffe, one of the founders of the TPTP library, to issue a challenge to OSCAR. At CADE-13, a competition was held for clausal-form theorem provers.2 Otter was one of the most successful contestants. In addition, Otter is able to handle problems stated in natural form (as opposed to clausal form), and Otter is readily available for different platforms.3 Sutcliffe selected 212 problems from the TPTP library, and suggested that OSCAR and Otter run these problems on the same hardware. This “Shootout at the ATP corral” took place, with the result that OSCAR was on the average 40 times faster than Otter. In addition, OSCAR was able to find proofs for 16 problems on which Otter failed, and Otter was able to find proofs for 3 problems on which OSCAR failed. Taking into account that Otter was written in C and OSCAR in LISP, the speed difference of the algorithms themselves could be as much as an order of magnitude greater. Apparently, natural deduction has some advantages over resolution-refutation.. (shrink)
