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) […]
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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COMP4418: Knowledge Representation and Reasoning Introduction to Prolog II Maurice Pagnucco School of Computer Science and Engineering University of New South Wales NSW 2052, AUSTRALIA morri@cse.unsw.edu.au Reference: Ivan Bratko, Prolog Programming for Artificial Intelligence, Addison- Wesley, 2001. Chapter 3. COMP4418 ⃝c UNSW, 2019 COMP4418, Monday 30 September, 2019 Introduction to Prolog II 1 Prolog
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Cooperative games COMP4418 Knowledge Representation and Reasoning Haris Aziz1,2 1School of Computer Science and Engineering, UNSW Australia 2Data61, CSIRO 2019 H. Aziz (UNSW) Cooperative games 2019 1 / 59 Outline 1 Coalitional games: introduction 2 Coalitional games: solution concepts 3 Coalitional games: representations 4 Coalitional games: computational issues 5 Conclusions H. Aziz (UNSW) Cooperative games
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COMP4418 ⃝c UNSW, 2019 COMP4418: Knowledge Representation and Reasoning Logic and Prolog Maurice Pagnucco School of Computer Science and Engineering University of New South Wales NSW 2052, AUSTRALIA morri@cse.unsw.edu.au COMP4418, Monday 30 September, 2019 Reasoning Under Uncertainty 1 Logic and Prolog Prolog stands for programming in logic How does the implementation of Prolog
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Chapter 5 Network Layer: The Control Plane Chapter 5: network layer control plane All material copyright 1996-2016 J.F Kurose and K.W. Ross, All Rights Reserved Chapter 5: outline Network-layer functions 5.1 introduction 5.5 5. 6 The SDN control plane Recall: two network-layer functions: 5. 2 routing protocols ICMP: The Internet Control Message Protocol forwarding:
Strictness of FOL To reason from P(a) to Q(a), need either • factsaboutaitself • universals,e.g.∀x(P(x)⊃Q(x)) – something that applies to all instances – all or nothing! But most of what we learn about the world is in terms of generics • e.g., encyclopedia entries for ferris wheels, violins, turtles, wildflowers Properties are not strict for
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COMP4418, 2019 – Exercises 1 Answer Set Programming 1.1 Modelling Let S = {s1,…,sn} be a set of sets. A set cover of S is a set C ⊆ S such that s∈S s = s∈C s. A k-set cover is a set cover of size k, that is, |C| = k. For instance, for
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Declarative language Before building system before there can be learning, reasoning, planning, explanation … need to be able to express knowledge Want a precise declarative language • declarative: believe P = hold P to be true cannot believe P without some sense of what it would mean for the world to satisfy P • precise:
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