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Integration of Inference and Machine Learning As a Tool for Creative Reasoning

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Integration of Inference and Machine Learning As a Tool for Creative Reasoning Modeling Changing Perspectives — Reconceptualizing Sensorimotor Experiences: Papers from the 2014 AAAI Fall Symposium Integration of Inference and Machine Learning as a Tool for Creative Reasoning Bartłomiej Snie´ zy˙ nski´ AGH University of Science and Technology al. Mickiewicza 30 30-059 Krakow, Poland e-mail: [email protected] Abstract MILS combines many knowledge manipulation tech- niques during reasoning. It is able to use a background In this paper a method to integrate inference and ma- knowledge, simple proof rules (such as generalization or chine learning is proposed. Execution of learning al- gorithm is defined as a complex inference rule, which modus ponens) or complex patterns (machine learning algo- generates intrinsically new knowledge. Such a solu- rithms) to produce information that was not stored explicite tion makes the reasoning process more creative and al- in the knowledge base. lows to re-conceptualize agent’s experiences depend- In the following sections related research is discussed, ing on the context. Knowledge representation used in the MILS model and inference algorithm are presented. the model is based on the Logic of Plausible Reason- Next, preliminary results of experiments: knowledge base ing (LPR). Three groups of knowledge transmutations and three use cases are described. are defined: search transmutations that are looking for the information in data, inference transmutations that Related research are formalized as LPR proof rules, and complex ones that can use machine learning algorithms or knowl- LPR was proposed by Alan Collins and Richard Michalski, edge representation change operators. All groups can who in 1989 published their article entitled ”The Logic of be used by inference engine in a similar manner. In Plausible Reasoning, A Core Theory” (Collins and Michal- the paper appropriate system model and inference al- ski 1989). The aim of this study was to identify patterns gorithm are proposed. Additionally, preliminary exper- of reasoning used by humans and create a formal system, imental results are presented. which would be able to represent these patterns. The basic operations performed on the knowledge defined in the LPR Introduction include: abduction and deduction – used to explain and predict the Traditional reasoning techniques applied in AI offer conver- characteristics of objects based on domain knowledge; gent interpretation of the stored knowledge, which does not provide new knowledge. Machine learning techniques may generalisation and specialisation – allow for generalisa- be creative and provide diversity but are not integrated with tion and refining of information by changing the set of inference process. In this paper a method to integrate these objects to which this information relates to a set larger or two approaches is proposed. Execution of learning algo- smaller; rithm is defined as a complex inference rule, which produces abstraction and concretisation – change the level of detail new knowledge. Such a solution allows to re-conceptualize in description of objects; agent’s experiences depending on the context. It is possible similarity and contrast – allow the inference by analogy to change perspective in which stored data is analyzed and or lack of similarity between objects. intrinsically new knowledge is generated. The experimental results confirming that the methods of The solution proposed is formulated as a Multistrategy reasoning used by humans can be represented in the LPR are Inference and Learning System (MILS). The idea is based presented in subsequent papers (Boehm-Davis, Dontas, and on the Inferential Theory of Learning (Michalski 1994). Michalski 1990a; 1990b). The objective set by the creators In this approach, learning and inference can be presented has caused that LPR is significantly different from other as a goal-guided exploration of the knowledge space using known knowledge representation methods, such as classi- operators called knowledge transmutations. As a base for cal logic, fuzzy logic, multi-valued logic, Demster - Shafer knowledge representation the Logic of Plausible Reasoning theory, probabilistic logic, Bayesian networks, semantic net- (LPR) (Collins and Michalski 1989) is used. However, it is works, ontologies, rough sets, or default logic. Firstly, there possible to apply this approach using other knowledge rep- are many inference rules in LPR, which are not present in resentation techniques, which are based on logic. the formalisms mentioned above. Secondly, many parame- Copyright c 2014, Association for the Advancement of Artificial ters are specified for representing the uncertainty of knowl- Intelligence (www.aaai.org). All rights reserved. edge. 33 On the basis of LPR, a DIH (Dynamically Interlaced Hi- Using relational symbols, formulas of LPR can be 0 erarchies) formalism was developed (Hieb and Michalski defined. If o; o ; o1; :::; on; a, a1; :::; an; v; c 2 C, 1993b; 1993a). Knowledge consists of a static part repre- v1; :::; vn are lists of elements of C, then V (o; a; v), sented by hierarchies and a dynamic part, which are traces, H(o1; o; c), B(o1; o), S(o1; o2; o; a), E(o1; a1; o2; a2), playing a role similar to statements in LPR. The DIH dis- V (o1; a1; v1) ^ ::: ^ V (on; an; vn) ! V (o; a; v) are LPR tinguishes three types of hierarchies: types, components and formulas. priorities. The latter type of hierarchy can be divided into The LPR language can be extended by adding countable subclasses: hierarchies of measures (used to represent the set of variables, which may be used instead of constant sym- physical quantities), hierarchies of quantification (allowing bols in formulas. quantifiers to be included in traces, such as e.g. one, most, or To manage uncertainty the following label algebra is all) and hierarchies of schemes (used as means for the defini- used: tion of multi-argument relationships and needed to interpret A = (A; ffri g): (1) the traces). A is a set of labels which estimate uncertainty of formulas. ITL was formulated just after DIH development (Michal- Labeled formula is a pair f : l where f is a formula and ski 1994). Michalski et al. also developed ITL implemen- l 2 A is a label. A set of labeled formulas can be considered tation - an INTERLACE system (Alkharouf and Michalski as a knowledge base. 1996). This system is based on DIH and can generate se- LPR inference patterns are defined as proof rules. Ev- quences of knowledge operations that will enable the deriva- ery proof rule ri has a sequence of premises (of length tion of a target trace from the input hierarchies and traces. pri ) and a conclusion. ffri g is a set of functions which Yet, not all kinds of hierarchy, probability and factors de- are used in proof rules to generate a label of a conclu- scribing the uncertainty of the information were included sion: for every proof rule ri an appropriate function fri : there. Also rule induction was not taken into account. pr A i ! A should be defined. For rule ri with premises p : l ; :::; p : l the plausible label of its conclusion Outline of the logic of plausible reasoning 1 1 n n is calculated using fri (l1; :::; ln). Examples of definitions MILS is based on LPR. It is formalized as a labeled deduc- of plausible algebras can be found in (Snie´ zy˙ nski´ 2001; tive system (LDS) (Gabbay 1991). If needed, instead of LPR 2002). another knowledge representation, which can be formulated There are five main types of proof rules: GEN, SP EC, using LDS, may be used. SIM, T RAN and MP . They correspond to the following The language consists of a finite set of constant symbols inference patterns: generalization, specialization, similarity C, five relational symbols and logical connectives: !, ^. transformation, transitivity of relations and modus ponens. The relational symbols are: V; H; B; S; E. They are used to Some transformations can be applied to different types of represent: statements (V ), hierarchy (H; B), similarity (S) formulas, therefore indexes are used to distinguish different and dependency (E). versions of rules. Formal definitions of these rules can be Statements are represented as object-attribute-value found in (Collins and Michalski 1989; Snie´ zy˙ nski´ 2003). triples: V (o; a; v), where o; a; v 2 C. It is a representation of the fact that object o has an attribute a equals v If object MILS Model o has several values of a, there should be several appropri- ate statements in a knowledge base. To represent vagueness MILS may be used to find an answer for a given hypothesis. of knowledge it is possible to extend this definition and al- The inference algorithm builds the proof using knowledge transmutations to infer the answer. It may also find substitu- low to use composite value [v1; v2; : : : ; vn], list of elements of C. It can be interpreted that object o has an attribute a tions for variables appearing in the hypothesis. Three types of knowledge transmutations are defined in MILS: equals v1 or v2, :::, or vn. Relation H(o1; o; c), where o1; o; c 2 C, means that o1 is • simple (LPR proof rules), o in a context c. Context is used for specification of the range • complex (using complex computations, e.g. rule induction of inheritance. o1 and o have the same value for all attributes algorithms or clustering methods) which depend on attribute c of object o. To show that one object is below the other in any hierar- • search (database or web searching procedures). chy, relation B(o1; o), where o1; o 2 C, should be used. Knowledge transmutation can be represented as a triple: Relation S(o1; o2; c) represents a fact, that o1 is similar to (p; c; a), where p are (possibly empty) premises or precon- o2; o1; o2; c 2 C. Context, as above, specifies the range of ditions, c is a consequence (pattern of formula(s) that can similarity.
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