VU @ D2.1.1 Part 1: Approximation Reasoning method Knowledge - PDF document

VU @ D2.1.1 Part 1: Approximation � Reasoning method Knowledge � Knowledge base Base � A-Box (UoM) and � T-Box Reasoning Input Output Method � Input 1

Guidelines for Reasoning Methods � Semantically well-founded providing a clear answer to the problem � Computationally attractive Knowledge resulting in an easier Base computation of approximate answers Reasoning � Improvable approximate Input Output Method answers � Dual sound and complete � Flexible to apply to different problems Reasoning Methods: Anytime Algorithms � Measurable Quality of the approximate result Quality of algorithm 1 � Recognizable Quality can be determined at run time 0.8 � Monotonicity over time and input quality 0.6 Quality � Consistency 0.4 � Diminishing returns with more improvements in the 0.2 beginning � Interuptibility at any time 0 0 1 2 3 4 5 6 7 � Preemptability ensures Algorithm step algorithm can be suspended and resumed 2

Anytime Algorithms for logical entailment � Boolean Constraint Propagation (BCP) sound but incomplete � Clausal BCP (restricted to clauses) ? � CNF-BCP false true � Prime-BCP (intractable) false S1 S3 � Formula BCP (intractable) � Fact Propagation x ¬x L � S1-/S3-entailment S sound and complete semantic approach Approximation for knowledge bases � “Compile” � a knowledge base Knowledge � into another one Base � with better computational properties Reasoning Input Output Method � Possibilities � Translate A-Box into a role-free ABox � Knowledge compilation 3

Approximation on A-Boxes Normal A-Box Role-Free A-Box Querying in Role-Free A-Boxes Instances to be tested if contained Query Instances contained in the query 4

Compiling the knowledgebase Knowledge Pre-Compile = Offline Reasoning Base++ Knowledge Base Reasoning Reasoning Input Output Input Output Method Method � Exact Knowledge Compilation � Approximate Knowledge Compilation Exact Knowledge Compilation Implicants D � Prime implica n ts D Σ v v v = and = Prime implicates Σ C = Con-/Disjunction of Literals Theory Σ � How to compute � Directly = � Derviable by unit resolution v v v � W.r.t. a tractable theory Implicats C 5

Approximate Knowledge Compilation � Classical approaches Lower Bound � Language Restriction (c.f. Role-Free A-Boxes) Theory Σ � Theory Approximation Upper Bound (TA) � Methods for TA: yes � Upper bound: UB Q = if UP Q then Σ Q = = No ≈ don’t care � Lower bound: no LB Q ≠ if LB Q then Σ Q ≠ ≠ Yes ≈ don’t care Anytime Variants of Exact Methods v v v Implicants D Lower Bound Theory Σ Theory Σ Upper Bound Implicats C v v v 6