Learning Prime Implicant Conditions from Interpretation Transition

Abstract

In a previous work we proposed a framework for learning normal logic programs from transitions of interpretations. Given a set of pairs of interpretations (I, J) such that J = TP (I), where TP is the immediate consequence operator, we infer the program P. Here we propose a new learning approach that is more efficient in terms of output quality. This new approach relies on specialization in place of generalization. It generates hypotheses by specialization from the most general clauses until no negative transition is covered. Contrary to previous approaches, the output of this method does not depend on variables/transitions ordering. The new method guarantees that the learned rules are minimal, that is, the body of each rule constitutes a prime implicant to infer the head.

Learning Dynamics with Synchronous, Asynchronous and General Semantics

“…A modeling of both synchronous, asynchronous and general semantics is also proposed. From this solid theory a rather straightforward extension of the LF1T algorithm of [13] is proposed. LF1T is restricted to learning synchronous deterministic Boolean systems.…”

“…The table also provides the number of transitions generated by the semantics for each benchmark. It is important to note that those systems are all synchronous deterministic, meaning that in the synchronous case, the input transitions of GULA are the same as the input transitions of LF1T in [13]. Here the number of transitions in the synchronous case is much lower than for the random experiment, which explains the difference in terms of run-time.…”

“…Furthermore the rules to be learned are quite simpler in the sense that the number of conditions (i.e., the size of the body of all rules) never exceed 6 and the total number of rules is always below 124. Nevertheless, the new algorithm is slower than LF1T [13] in the synchronous deterministic Boolean case, which is expected since it is not specifically dedicated to learning such networks: GULA learns both values (0 and 1) of each variable and pre-processes the transitions before learning rules, while LF1T is optimized to only learn rules that make a variable take the value 1 in the next state. On the other hand, asynchronous and general semantics transitions can only be handled by our new algorithm.…”

“…Table 1 shows the run time of GULA when learning Boolean networks from [4]. Here we reproduced the experiments held in [13]: all transitions of each benchmark are generated but only for the three considered semantics. The table also provides the number of transitions generated by the semantics for each benchmark.…”

Learning Delayed Influences of Biological Systems

“…To build a logic program with LF1T , we use a bottom-up method that generates hypotheses by specialization from the most general rules that are fact rules, until the logic program is consistent with all input state transitions. Learning by specialization ensures to output the most general valid hypothesis (Ribeiro and Inoue, 2014 ). Here, the notion of prime implicant is used to define minimality of logic programs.…”