Integrating Abduction and Induction in AI Edinburgh UK
Integrating Abduction and Induction in AI, Edinburgh, UK, July 29, 2005 Inductive Generalizations and Manipulative Abduction Department of Philosophy and Computational Philosophy Laboratory, University of Pavia, Italy Department of Philosophy, Sun Yat-sen University, Canton, China
Integrating Induction and Abduction • Induction in Organic Agents • Mimetic Inductions • Ideal and Computational Inductive Agents • Mimetic Abductions • Ideal and Computational Abductive Agents • Sentential, Model-Based and Manipulative Abduction • A Cognitive Integration: Samples, Induction, and Abduction
Organic Induction The Human agent is Human beings mess thing up genetically and culturally above the simplest levels of endowed with a kind of complexity. This is particularly Van Benthem (2000) Induction rationaland survival kit true of inductive inferences : iton Abduction kid on touching the (Woods, 2004) also seems there • is a. The tendency for element his to mother’s containing some strategic • Indeed, it is noton easy give a crystal-clear hasty and unfounded kitchen stove learns inuses one of fallacies. definition of them, either independently or in generalizations. case never to do that again this is not their inter-relationship. (Of course, For example: But not every generalization (primitive induction) easy for “Deduction” either) Deduction from a single case is bad (that Hasty This is not an offense to generalization is a fallacy). Hasty inductive reasoning. in Organic 1. Agents Cynthia is a bad driver. generalization Induction is a prudent strategy, especially when risks MILL provides “Methods” for 2. Women are bad drivers. are high: skills are • survival Hasty. Induction Generalization, Secundum Quid, Biased sometimes exercised. Other Fallacies 3. It is sometimes worse not Statistics, PEIRCE integrates and to generalize in this way. successfully but not rationally. Abduction • a. Strategic versus Rationalthe thinking (conscious Induction We have cognitive error through but often tacit) syllogistic where not a strategic error. This framework fact the two non-deductive always • stimulated Mill says the that institutions rather than inferences can be clearly theorists to say something individuals are the embodiment of inductive distinguished. helpful about the problem of logics induction – MILL - (and on abduction - PEIRCE) both fallacious but strong.
Mimetic Induction – Mimetic Abduction Ideal Agents • Kid’s performance is a strategic success and a cognitive failure. • Human beings are hardwired for survival and for truth alike so best strategies can be built and made explicit, through self-correction and re-consideration (for example Mill’s methods). • Mill’s methods for induction, Peirce’s syllogistic and inferential models for abduction Inductive and Abductive Agents • Ideal Logical Inductive and Abductive Agents • Ideal Computational Inductive, Abductive, and Hybrid Agents • Merely successful strategies are replaced with successful strategies that also tell the more precise truth about things.
creative, selective • what is abduction? • theoretical abduction (sentential, model-based) scientific discovery diagnosis • manipulative abduction (mathematical diagrams, construals)
creative, selective • what is abduction? • theoretical abduction (sentential, model-based) scientific discovery diagnosis • manipulative abduction (mathematical diagrams, construals)
SENTENTIAL Theoretical Abduction MODEL-BASED
Model-based cognition • Simulative reasoning • Analogy SENTENTIAL • Visual-iconic reasoning • Spatial thinking Peirce stated that all thinking is • Thought in signs, experiment sense activities and signs can be icons, indices, • Perception, or • Visual imagery symbols. Moreover, all inference is a • Deductive reasoning(Beth’s form of sign activity, where the method word of semantic tableaux, sign includes “feeling, image, Girard’s “geometry” of proofs, etc. ) • Emotion conception, and other representation” Theoretical Abduction (CP 5. 283), and, in Kantian words, all synthetic forms of cognition. That is, a considerable part of the thinking activity is model-based. Of course modelbased reasoning acquires its peculiar MODEL-BASED creative relevance when embedded in abductive processes
Mathematical Diagrams (also Model-Based) manipulative abduction nicely introduces to hypothesis generation in active, distributed, and embodied cognition The activity of “thinking through doing” is made possible not simply by mediating cognitive artifacts and tools, but by active process of testing and manipulation. Thinking through doing Construals Manipulative Abduction
Thinking through doing Construals Manipulative Abduction
Samples, Induction, Abduction “If we think that a sampling “If we do not think of inductive method is fair and unbiased, generalizations as abductions then straight generalization we are at a loss to explain why gives the best explanation of the such inference is made stronger sample frequencies. But if the and more warranted, if in size is small, alternative connecting data we make a explanations, where the systematic search for counterfrequencies differ, may still be instances and cannot find any, plausible. These alternative than it would be just take the explanations become less and observation passively. Why is less plausible as the sample size the generalization made Manipulative abduction can be considered a kind grows, because theand sample stronger byof making an effort to • Samples Manipulative Abduction basisbeing for further meaningful inductive generalizations. unrepresentative due to examine a wide variety of types For example different construals give rise. The tothe chance becomes more and morecanabduction of A’s? answer is way that for it is • Construals Manipulative is correct improbable. Thus viewing made stronger because the different inductive generalizations. If “an describing the features of what areinductive called ``smart inductive generalization as the active search of generalization is an inference that goesfailure from the generalizations'', as contrasted to the of trivial ones. For abductions show why sample counter-instances tend to rule characteristics of some observed samples of individuals example, in science construals can shed light on this process size is important. Again, we see and ``appraisal'': out various hypotheses about of sample through to a conclusion about``production'' the distribution of those that analyzing inductive ways in which the sample might construals, manipulative creative abduction generates characteristics in some larger populations” generalizations as abductions be biased, can thatoriginate is, is abstract hypotheses butthe in the meantime (Josephson) what characterizes sample as shows us how tobases evaluate the strengthens the abductive possible for further meaningful inductive “representative” is itsinferences effect (sample frequency) byruling out strengths of these conclusion of by generalizations through the identification new samples (Josephson , ofp. new 42). ” alternative explanations for the reference to(or part of its cause (populations frequency): features of already available sample, for instance observed this should be considered a conclusion about itsfrequency cause. (Josephson in terms of the detection of relevant circumstances). Different generated construals 2000)” can give rise to different plausible inductive generalizations.
LOGICAL IDEAL ABDUCTIVE and INDUCTIVE SYSTEMS Flach and Kakas (2000). A useful - symbolic : they activate and “anchor” meanings in material perspective on integration of communicative andand intersubjective mediators in the abduction induction: framework of the phylogenetic, ontogenetic, and cultural • explanation (hypothesis does not reality • of cf. thethe human being and its language. They analysis of refer tocognitive observables – selective originatedabduction in origin embodied cognitioncreates and gestures we share the of theabduction [but with some mammals but also non mammals animals (cf. mathematical continuous new hypotheses too]) monkey knots pigeon categorization, Grialou, Longo, line asand a pre-conceptual • generalization – genuinely new invariant and Okada, 2005); of three cognitive (hypothesis can entail additional practices 2005), are in turn sets of proof invariants, • (Theissier, logical systems observable information on - abstractand : they arenumeric based on independence of the linea maximal sets of structures that are preserved from one proof unobserved individual, extending regarding(Châtelet, sensory 1993; modality; strongly stabilize experience Dehaene, to another or which are preserved by proof theory T) and common categorization. The maximality especially 1997; Butterworth, 1999). transformations. They are theisresult of a distilled praxis ofand proof: it is made of maximally Imagine wepraxis, have athe new abductive important: it refers to their practical historical regularities. by theory T’ =stable T H constructed invariance and stability; induction: an inductive extension -rigorous: ofthe rigor can of proof is reached through a difficult a theory be viewed as set of practical experience. For instance, in MEMORYLESSNESS the case of abductive of the OF • estensions MAXIMIZATION characterizes original T. mathematics, as theory thedemonstrative maximal place for convincing reasoning. Its properties do not yield information the past, contrarily for fact instance to reasoning. Rigor lies in of proofs and in the controversies onthe IAIstability areabout of course the narrative and not logical descriptions of nonthey can be iterated. open and alive demonstrative processes, which often involve Mathematics is the best example of maximal stability andmemories. “historical”, “contextual”, and “heuristic” conceptual invariance.
Thanks lorenzo. magnani@unipv. it
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