Goal Deductive reasoning in language as close as possible to full FOL ! ! ¬,∧,∨,∃,∀ Knowledge Level: ! ! or! ! given KB, α, determine if KB |= α. given an open α(x1,x2,…xn), find t1,t2,…tn such that KB |= α(t1,t2,…tn) When KB is finite {α1, α2, …, αk} !! KB|=α iff ! iff ! iff […]
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Declarative / procedural Theorem proving (like resolution) is a general domain-independent method of reasoning Does not require the user to know how ! knowledge will be used ! willtryalllogicallypermissibleuses Sometimes have ideas about how to use knowledge, how to search for derivations ! do not want to use arbitrary or stupid order Want to communicate
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Resource Allocation COMP4418 Knowledge Representation and Reasoning Haris Aziz1 1School of Computer Science and Engineering, UNSW Australia 1 How to assign donated kidneys? 2 How to allocate tasks to drones? 3 How to match employers to employees? 4 Outline Allocation setting Efficiency concepts Fairness concepts Other properties of mechanisms Allocation of indivisible items under ordinal
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Path Finding, what’s new since A*? Abdallah Saffidine The University of New South Wales, Sydney, Australia August 20, 2019 1/26 2/26 Outline A* setup and limitations Beyond A* research topics Multi-Agent Pathfinding 3/26 The classical A* setup 4/26 The classical A* setup Unnecessary requirements Complete (always finds a solution) Optimal (solution is always the best
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CSE 521: Design & Analysis of Algorithms I NP-completeness Paul Beame 1 Computational Complexity Classify problems according to the amount of computational resources used by the best algorithms that solve them Recall: worst-case running time of an algorithm max # steps algorithm takes on any input of size n 2 Relative
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School of Computer Science and Engineering COMP4418: Knowledge Representation and Reasoning COMP4418: Knowledge Representation and Reasoning Lecturers: • Haris Aziz (K17-L3; Haris.Aziz@unsw.edu.au) • Maurice Pagnucco (Lecturer-in-Charge; J17-501B; morri@cse.unsw.edu.au) • Abdallah Saffidine (K17-501B; abdallahs@cse.unsw.edu.au) Aim: Introduce • Techniques used in KR to represent knowledge • Associated methods of automated reasoning Units of Credit: 6 Prerequisites: COMP3411
Answer Set Programming1 Abdallah Saffidine COMP4418 1Slides designed by Christoph Schwering Non-Monotonic Reasoning 2 / 30 Non-Monotonic Reasoning ∀x (Car(x) → ¬Entry(x)) 2 / 30 Non-Monotonic Reasoning ∀x (Car(x) → ¬Entry(x)) ∀x (Car(x) ∧ Auth(x) → Entry(x)) 2 / 30 Non-Monotonic Reasoning ∀x (Car(x) → ¬Entry(x)) ∀x (Car(x) ∧ Auth(x) → Entry(x)) |= Car(C)∧Auth(C)
Knowledge Representation and Reasoning Several of the lectures in the first section of this course are based on the following book: ! Ronald Brachman & Hector Levesque ! Knowledge Representation and Reasoning ! Morgan Kaufmann, 2004. ! ISBN: ISBN: 978-1-55860-932-7. These slides will be clearly identified. Up-to-date slides for this book are available from: !
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Limit expressive power? Defaults, probabilities, etc. can all be thought of as extensions to FOL, with obvious applications Why not strive for the union of all such extensions? ! a language co-extensive with English? Problem: automated reasoning Lesson here: ! reasoning procedures required for more expressive languages may not work very well in practice Tradeoff:
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Horn clauses Clauses are used two ways: • asdisjunctions:! (rain∨sleet) • asimplications:! (¬child∨¬male∨boy) Here focus on 2nd use Horn clause = at most one +ve literal in clause • positive / definite clause = exactly one +ve literal ! [¬p1, ¬p2, …, ¬pn, q] • negative clause = no +ve literals ! [¬p1, ¬p2, …,
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