Tree Adjoining Grammars, Language Bias, and Genetic Programming Nguyen Xuan Hoai 1 , R.I. McKay 2 , and H.A. Abbass 2 School of Computer Science, Australian Defence Force Academy, ACT 2600, Australia 1 x.nguyen@student.adfa.edu.au, 2 rim, abbass@cs.adfa.edu.au Abstract. In this paper, we introduce a new grammar guided genetic programming system called tree-adjoining grammar guided genetic programming (TAG3P+), where tree-adjoining grammars (TAGs) are used as means to set language bias for genetic programming. We show that the capability of TAGs in handling context-sensitive information and categories can be useful to set a language bias that cannot be specified in grammar guided genetic programming. Moreover, we bias the genetic operators to preserve the language bias during the evolutionary process. The results pace the way towards a better understanding of the importance of bias in genetic programming. 1 Introduction The use of bias has been a key subject in inductive learning for many years [13]. Theoretical arguments for its necessity were presented in [20, 23]. Bias is the set of factors that influence the selection of a particular hypothesis; therefore, some hypotheses are preferred over others [18]. Three main forms of bias can be distinguished [21]: selection, language and search bias. In selection bias, the criteria for selecting a hypothesis create a preference ordering over the set of hypothesis in the hypothesis space. A language bias is a set of language-based restrictions to represent the hypothesis space. A search bias is the control mechanism for reaching one hypothesis from another in the hypothesis space. A bias can be either exclusive or preferential. An exclusive bias eliminates certain hypotheses during the learning process, whereas a preferential bias weights each hypothesis according to some criteria. An inductive bias is said to be correct when it allows the learning system to elect the correct target concept(s) whereas an incorrect bias prevents the learning system from doing so. An inductive bias is said to be strong when it focuses the search on a relatively small portion of the space; and weak when it focuses the search on a large portion of the hypothesis space. A declarative bias in an inductive learning system is one specified explicitly in a language designed for the purpose; if the bias is simply encoded implicitly in the search mechanism, it is said to be procedural. An inductive bias is static if it does not change during the learning process; otherwise it is dynamic. A genetic programming (GP) system [1, 11] can be seen as an inductive learning system. In a GP system, fitness-based selection, the bias towards programs that