One of the most important tasks in database technology is to combine the following activities: data mining or inferring knowledge from data and query processing or reasoning on acquired knowledge. The solution of this task requires a logical language with unified syntax and semantics for integrating deductive (using knowledge) and inductive (acquiring knowledge) reasoning. In this paper, we propose a unified model of commonsense reasoning. We also demonstrate that a large class of inductive machine learning (ML) algorithms can be transformed into the commonsense reasoning processes based on wellknown deduction and induction logical rules. The concept of a good classification (diagnostic) test (Naidenova & Polegaeva, 1986) is the basis of our approach to combining deductive and inductive reasoning.
One of the most important tasks in database technology is to combine the following activities: data mining or inferring knowledge from data and query processing or reasoning on acquired knowledge. The solution of this task requires a logical language with unified syntax and semantics for integrating deductive (using knowledge) and inductive (acquiring knowledge) reasoning.
In this paper, we propose a unified model of commonsense reasoning. We also demonstrate that a large class of inductive machine learning (ML) algorithms can be transformed into the commonsense reasoning processes based on well-known deduction and induction logical rules. The concept of a good classification (diagnostic) test (Naidenova & Polegaeva, 1986) is the basis of our approach to combining deductive and inductive reasoning.
The unique role of the good test’s concept is explained by the equivalence of the following relationships (Cosmadakis et al., 1986):
Functional/implicative dependencies between attributes/values of attributes;
Partition dependencies between classifications generated by attributes (attributes’ values) on a set of objects descriptions.
The task of inferring good diagnostic tests is formulated as the search for the best approximations of a given classification (a partitioning) on a given set of objects’ examples. It is this task that some well known ML problems can be reduced to (Naidenova, 1996): finding keys and functional dependencies in database relations, finding implicative dependencies and association rules, inferring logical rules (if-then rules, rough sets, and “ripple down” rules) and decision tree from examples, learning by discovering concept hierarchies, and some others.
The analysis of ML algorithms in the framework of good tests inferring and their decomposition to subtasks and elementary operations made it possible to see that they are the processes of interconnected deductive and inductive commonsense reasoning.Top
There is not an exact definition of commonsense reasoning. This area of research covers a wide range of topics: default reasoning (Sakama, 2005), active agent’s reasoning (Thomason, 2007) and some others, for instance, qualitative reasoning, everyday thought about physical systems, spatial reasoning (Mueller, 2006).
Traditionally, commonsense reasoning is considered only as deduction (using knowledge). Induction of new knowledge from observations is considered in the framework of ML problems. That’s why many efforts are made in order to combine inductive and deductive reasoning. Two basic ways for this goal exist: 1) to aggregate into a whole system some well-known models of ML and deductive reasoning (Lavrac & Flash, 2000); 2) to enlarge the logic programming language to support both types of inference in a single formalism (Aragão, & Fernandes, 2004), (Sakama, 2005), (Galitsky et al., 2005), (Lisi, 2006). These approaches are very promising. However, the theoretical basis of these works is first-order predicate calculus with predicate as the main element of knowledge description while the main element of commonsense reasoning is concept.
We propose a model of commonsense reasoning based on processes of classification. Knowledge in this model is a system of coordinated links: objects ↔ classes of objects, classes of objects ↔ properties, objects ↔ properties. For instance, “all squares are rhombs”, “square is a rhomb”, “all the angles of rectangle are right”, “square is a rhomb all the angles of which is right”, “if the sun is in the sky and not raining, then the weather is good”, “conifers are pine-tree, fir-tree, cedar”. These connections have causal nature and can be formally expressed with the aid of implications. By commonsense reasoning we understand constructing and using the coordinated classification connections between objects, properties and classes. This understanding goes back to the work of Jean Piaget & Bärvel Inhelder (1959).
Key Terms in this Chapter
The Subtask of the Second Kind: For a given set of positive and negative examples and a non-empty collection of attributes’ values such that it is not a test for the set of positive examples, find all GMRTs (GIRTs) containing it.
The Subtask of the First Kind: Assume that we have two sets of positive and negative examples and a positive example. The subtask of the first kind is to find all the collections of attributes’ values that are included in the description of this example and correspond to the good tests (GNRTs or GIRTs) for the set of positive examples.
Inductive Transitions: These are the processes of extending or narrowing collections of values (objects). They can be smooth and boundary. Upon smooth transition, a certain assigned property of the generated collections does not change. Upon boundary transition, a certain assigned property of the generated collections changes to the opposite one.
Good Classification Test: A classification test for a given set of positive examples is good if this set is maximal in the sense that if we add to it any positive example, then the collection of attributes’ values describing the obtained set will describe at least one negative example.
Implicative Assertions: Implications describe the regularities mutually connecting objects, properties and classes of objects. They can be given explicitly by an expert or derived automatically from examples via some learning process.
Good Irredundant Test (GIRT): A good test is irredundant if deleting any attribute’s value from it changes its property “to be test” into the property “not to be a test”.
Good Maximally Redundant Test (GMRT): A good test is a maximally redundant if extending it by any attribute’s value not belonging to it changes its property “to be a good test” into the property “to be test but not a good one”.
Diagnostic or Classification Test: Assume that we have two sets of objects’ examples called positive and negative examples respectively. A test for a subset of positive examples is a collection of attributes’ values describing this subset of examples if it is unique, i. e. none of the negative examples is described by it.
Commonsense Reasoning Rules (CRRs): These are rules with the help of which implicative assertions are used, updated and inferred from examples. The deductive CRRs are based on the use of syllogisms: modus ponens, modus ponendo tollens, modus tollendo ponens, and modus tollens. The inductive CRRs are the canons formulated by J. S. Mill (1900). Commonsense reasoning is based on using the CCRs.