Extending the Knowledge Compilation Map: Krom, Horn, Affine and Beyond
نویسندگان
چکیده
We extend the knowledge compilation map introduced by Darwiche and Marquis with three influential propositional fragments, the Krom CNF one (also known as the bijunctive fragment), the Horn CNF fragment and the affine fragment (also known as the biconditional fragment) as well as seven additional languages based on them, and composed respectively of Krom or Horn CNF formulas, renamable Horn CNF formulas, disjunctions of Krom CNF formulas, disjunctions of Horn CNF formulas, disjunctions of Krom or Horn CNF formulas, disjunctions of renamable Horn CNF formulas, and disjunction of affine formulas. Each fragment is evaluated w.r.t. several criteria, including the complexity of basic queries and transformations, and its spatial efficiency is also analyzed.
منابع مشابه
Disjunctive closures for knowledge compilation
The knowledge compilation (KC) map [1] can be viewed as a multi-criteria evalu-ation of a number of target classes of representations for propositional KC. Usingthis map, the choice of a class for a given application can be made, consideringboth the space efficiency of it (i.e., its ability to represent information using lit-tle space), and its time efficiency, i.e., the queries...
متن کاملExistential Closures for Knowledge Compilation
We study the existential closures of several propositional languages L considered recently as target languages for knowledge compilation (KC), namely the incomplete fragments KROM-C, HORN-C, K/H-C, renH-C, AFF, and the corresponding disjunction closures KROM-C[∨], HORN-C[∨], K/H-C[∨], renH-C[∨], and AFF[∨]. We analyze the queries, transformations, expressiveness and succinctness of the resultin...
متن کاملBoolean Affine Approximation with Binary Decision Diagrams
Selman and Kautz’s work on knowledge compilation has established how approximation (strengthening and/or weakening) of a propositional knowledgebase can be used to speed up query processing, at the expense of completeness. In the classical approach, the knowledge-base is assumed to be presented as a propositional formula in conjunctive normal form (CNF), and Horn functions are used to overand u...
متن کاملBinary Decision Diagrams for Affine Approximation
Selman and Kautz’s work on “knowledge compilation” established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this classical approach, querying uses Horn overand under-approximations of a given knowledge-base, which is represented as a propositional formula in conjunctive normal fo...
متن کاملInformation loss in knowledge compilation: A comparison of Boolean envelopes
Since Selman and Kautz’s seminal work on the use of Horn approximation to speed up the querying of knowledge bases, there has been great interest in Boolean approximation for AI applications. There are several Boolean classes with desirable computational properties similar to those of the Horn class. The class of affine Boolean functions, for example, has been proposed as an interesting alterna...
متن کامل