# Abductive Concept Learning Task

An Abductive Concept Learning (ACL) Task is a Abductive Reasoning Task that allows the learner to learn from incomplete information.

**Context:**- It can be defined as an extension of Inductive Logic Programming Task that can learn using a Abductive Reasoning Task.
- It can be solved by a Abductive Concept Learning System by implementing a Abductive Concept Learning Algorithm.

**Example(s):****Counter-Example(s):****See:**Non-Monotonic Reasoning, Most Economical Explanation, Explanation-based Learning, Explanation-Based Learning, Inductive Logic Programming, Set Cover Problem, Occam's Razor, Prior Probability, Proof Theory, Sequent Calculus, Analytic Tableaux, Modal Logic, Abductive Logic Programming.

## References

### 2017

- (Kakas, 2017) ⇒ Antonis C. Kakas. (2017). “Abduction”. In: (Sammut & Webb, 2017) DOI:10.1007/978-1-4899-7687-1_1
- QUOTE: Abductive concept learning (ACL) (Kakas and Riguzzi 2000) is a learning framework that allows us to learn from incomplete information and to later be able to classify new cases that again could be incompletely specified. Under ACL, we learn abductive theories, [math]\langle T, A, IC\rangle[/math] with abduction playing a central role in the covering relation of the learning problem. The abductive theories learned in ACL contain both rules, in [math]T[/math] , for the concept(s) to be learned as well as general clauses acting as integrity constraints in [math]IC[/math].
Practical problems that can be addressed with ACL: (1) concept learning from incomplete background data where some of the background predicates are incompletely specified and (2) concept learning from incomplete background data together with given integrity constraints that provide some information on the incompleteness of the data. The treatment of incompleteness through abduction is integrated within the learning process. This allows the possibility of learning more compact theories that can alleviate the problem of over fitting due to the incompleteness in the data. A specific subcase of these two problems and important third application problem of ACL is that of (3) multiple predicate learning, where each predicate is required to be learned from the incomplete data for the other predicates. Here the abductive reasoning can be used to suitably connect and integrate the learning of the different predicates. This can help to overcome some of the nonlocality difficulties of multiple predicate learning, such as order-dependence and global consistency of the learned theory.

ACL is defined as an extension of Inductive Logic Programming (ILP) where both the background knowledge and the learned theory are abductive theories. The central formal definition of ACL is given as follows where examples are atomic ground facts on the target predicate(s) to be learned.

- QUOTE: Abductive concept learning (ACL) (Kakas and Riguzzi 2000) is a learning framework that allows us to learn from incomplete information and to later be able to classify new cases that again could be incompletely specified. Under ACL, we learn abductive theories, [math]\langle T, A, IC\rangle[/math] with abduction playing a central role in the covering relation of the learning problem. The abductive theories learned in ACL contain both rules, in [math]T[/math] , for the concept(s) to be learned as well as general clauses acting as integrity constraints in [math]IC[/math].

### 2000

- (Kakas & Riguzzi, 2000) ⇒ Antonis C. Kakas, and Fabrizio Riguzzi (2000). "Abductive concept learning". New Generation Computing, 18(3), 243-294.DOI: 10.1007/BF03037531
- QUOTE: An algorithm for ACL is developed by suitably extending the top-down ILP method: the deductive proof procedure of Logic Programming is replaced by an abductive proof procedure for Abductive Logic Programming. This algorithm also incorporates a phase for learning integrity constraints by suitably employing a system that learns from interpretations like ICL. The framework of ACL thus integrates the two ILP settings of explanatory (predictive) learning and confirmatory (descriptive) learning. The above algorithm has been implemented into a system also called ACL Several experiments have been performed that show the effectiveness of the ACL framework in learning from incomplete data and its appropriate use for multiple predicate learning.