1. ©Agent Technology, 2008, Ai Lab NJU Agent Technology Agent model and theory

2. Nov., 2008 ©Gao Yang, Ai Lab NJU 2 Agent model and theory 6.1 Logical Background – 6.1.1 Basic Concepts – 6.1.2 Propositional and Predicate Logic – 6.1.3 Modal Logic – 6.1.4 Dynamic Logic – 6.1.5 Temporal Logic 6.2 Cognitive Primitives – 6.2.1 Knowledge and Beliefs – 6.2.2 Desires and Goals – 6.2.3 Intentions

3. Nov., 2008 ©Gao Yang, Ai Lab NJU 3 Chapter 4: Agent model and theory – 6.2.4 Commitments – 6.2.5 Know-how 6.3 Belief Revision – 6.3.1 AGM Framework – 6.3.2 Epistemic entrenchment 6.4 Social Primitives – 6.4.1 Team and Organizational Structure – 6.4.2 Mutual Beliefs and Joint Intentions – 6.4.3 Social Commitments – 6.4.4 Group Know-how and Intentions

4. Nov., 2008 ©Gao Yang, Ai Lab NJU 4 6.1 Logical Background 6.1.1 Basic Concepts – Why need formal method? As internal specification languages to be used by the agent in its reasoning or action; As external metalanguages to be used by the designer to specify, design, and verify certain behavioral properties of agents situated in a dynamic environment. – Differents between these languages One would like to have the same logical language server both of the above purpose. The internal language should be computationally efficient. The external language should be more expressive.

5. Nov., 2008 ©Gao Yang, Ai Lab NJU 5 6.1 Logical Background 6.1.1 Basic Concepts – Three aspects to logic Well-formed formulas: some statements; Proof-theory: is also called the syntax; Model-theory: is also called the semantics. – Purpose of the semantics

6. Nov., 2008 ©Gao Yang, Ai Lab NJU 6 6.1 Logical Background 6.1.2 Propositional and Predicate Logic – How to use this logic in agent Is simplest Represent factual information, often about the agents’ environment. – Example 6.1 The facts “it rains” and ‘road is wet”; Atomic propositions – Rain – Wet-road Implication that “if it rains, then the road is wet” can be captured by the propositional formula – Rain -> wet-road

7. Nov., 2008 ©Gao Yang, Ai Lab NJU 7 6.1 Logical Background 6.1.2 Propositional and Predicate Logic – The language of propositional logic Assume a set is given atomic propositions; SYN-1. SYN-2. – The formal model Let L identifies the set of atomic propositions that are true. SEM-1. SEM-2. SEM-3.

8. Nov., 2008 ©Gao Yang, Ai Lab NJU 8 6.1 Logical Background 6.1.2 Propositional and Predicate Logic – Imply is true if p is false irrespective of q – Predicate logic Do not use predicate logic in the specification language. Use it in metalanguage, which is used in semantic conditions. Universal quantifier Existential quantifier

9. Nov., 2008 ©Gao Yang, Ai Lab NJU 9 6.1 Logical Background 6.1.3 Modal Logic – Objective To investigate different modes of truth, such as possibly true and necessarily true. In agents’ study, it is used to give meaning to concepts such as belief and knowledge. – Modal language Classical propositional logic is extended with two modal operators: for possibility and for necessity. SYN-3. SYN-6.

10. Nov., 2008 ©Gao Yang, Ai Lab NJU 10 6.1 Logical Background 6.1.3 Modal Logic – Example 6.2 “it is possible that it rains” as “it is necessary that the sun rises in the east” as – Model is the set of the worlds gives the set of formulas true at a world is an accessibility relation SEM-6.

11. Nov., 2008 ©Gao Yang, Ai Lab NJU 11 6.1 Logical Background SEM-5. SEM-6. SEM-8. – Algebric properties of the accessibility relation R is reflexive iff R is serial iff R is transitive iff R is symmetric iff R is euclidean iff

12. Nov., 2008 ©Gao Yang, Ai Lab NJU 12 6.1 Logical Background 6.1.4 Dynamic Logic – What is dynamic logic Can be thought of as the modal logic of action The necessity and possibility of dynamic logic are based upon the kinds of actions available Can be used in a number of areas of DAI. – Model Language and its sublanguage Sublanguage define action regular expressions is a set of atomic action symbols SYN-5. SYN-6.

13. Nov., 2008 ©Gao Yang, Ai Lab NJU 13 6.1 Logical Background SYN-6. SYN-8. SYN-9. Notes: – a;b means doing a and b in sequence. – a+b means doing either a or b. – p? is an action based on confirming the truth value of proposition p. – a* means 0 or more (but finitely many) iterations of a. – Example 6.3 “If q then a else b endif”

14. Nov., 2008 ©Gao Yang, Ai Lab NJU 14 6.1 Logical Background – Model Here W, L defined as model logic; Is a transition relation. RP-1. RP-2. RP-3. RP-6. SEM-9. SEM-10.

15. Nov., 2008 ©Gao Yang, Ai Lab NJU 15 6.1 Logical Background 6.1.5 Temporal Logic – Several variants about temporal logic Linear versus Branching Discrete versus Dense Moment-Based versus Period-Based – Some terms in temporal logic Moments: associated with possible state of the world, has a strict partial order. Path: set of moments containing the given moments.

16. Nov., 2008 ©Gao Yang, Ai Lab NJU 16 6.1 Logical Background

17. Nov., 2008 ©Gao Yang, Ai Lab NJU 17 6.1 Logical Background – Linear-time temporal logic language SYN-10. SYN-11. Notes: – means at a moment t on a path, q holds at a future moment t’ on the given path, and p holds on all moments between t and t’. – means p holds sometime in the future on the given path and abbr. with. – means p always holds in the future on the given path – means p holds in the next moment. – means q held in a past moment.

18. Nov., 2008 ©Gao Yang, Ai Lab NJU 18 6.1 Logical Background – Model Here T is the set of moments, < the temporal ordering relation, and gives the denotations of the atomic propositions. SEM-11. SEM-12. SEM-13. Note: M3 is linear, < is a total ordering.

19. Nov., 2008 ©Gao Yang, Ai Lab NJU 19 6.1 Logical Background (optional) – Branching temporal and Action logic Builds on top of and, especially uses the ideas of the well-known language CTL*. captures the essential properties of actions and time that are of value in specifying agents. SYN-12. SYN-13. SYN-16. SYN-15. SYN-16.

20. Nov., 2008 ©Gao Yang, Ai Lab NJU 20 6.1 Logical Background (optional) – Notes about syntax The branching-time operator, A, denotes “in all paths at the present moment.” E, denotes “in some path at the present moment.” R, denotes “in the real path at the present moment.” The constructor (V a:p) means that “there is an action under which p becomes true.” – Examples 6.4 EFr, AF(q v r), RFq hold at t 0. E r, A[a]q, A[d](q v r), A[e]true hold at t 0. (V e: Ex true ^ Ax[e]q) holds at t 0.

21. Nov., 2008 ©Gao Yang, Ai Lab NJU 21 6.1 Logical Background (optional) – Model SEM-16. SEM-15. SEM-16. SEM-18. SEM-19. SEM-20. SEM-21.

22. Nov., 2008 ©Gao Yang, Ai Lab NJU 22 6.1 Logical Background (optional) SEM-22. SEM-23. SEM-26. SEM-25. SEM-26. SEM-28.

23. Nov., 2008 ©Gao Yang, Ai Lab NJU 23 6.2 Cognitive Primitives Origin – Intentional stance – Knowledge level – Functional level BDI logic – Be used to reason about agent – Their beliefs, intentions, and actions bring about the satisfaction of their desires

24. Nov., 2008 ©Gao Yang, Ai Lab NJU 24 6.2 Cognitive Primitives Modal operators – Bel(belief), Des(desire), K h (know-how) and Int(intention) – SYN-18. Semantics for Example 6.5 – Consider an agent who has the desire to win a lottery eventually and intends to buy a lottery ticket sometime, but does not believe that will ever win the lottery.

25. Nov., 2008 ©Gao Yang, Ai Lab NJU 25 6.2 Cognitive Primitives 6.2.1 Knowledge and Beliefs – B, a belief accessibility relation, which behaves as a modal necessity operator, – Knowledge(know-that), is customarily defined as a true belief. – B is serial, symmetric, euclidean and reflecive. – SEM-29. – B depends on the given moments, and agent can change its beliefs over time.

26. Nov., 2008 ©Gao Yang, Ai Lab NJU 26 6.2 Cognitive Primitives 6.2.2 Desires and Goals – D, a desire accessibility relation, which represent the desires of the agent. – SEM-30. – In the philosophical view Desires can be inconsistent Agent need not know the means of achieving these desires – The role of desires According to inputs, agent choose a subset of desires that are both consistent and achievable – Goals The consistent achievable desires are usually called goals.

27. Nov., 2008 ©Gao Yang, Ai Lab NJU 27 6.2 Cognitive Primitives 6.2.3 Intentions – I, a intend accessibility relation, defined as the conditions that inevitably hold on each of the selected paths. – SEM-31. – Example 6.6 Consider next figure, assume that –r and –p hold everywhere other than as shown. Let the agent x at moment t0 prefer the path S1 and S2. Then, we have that x intend q (because it occurs eventually on both the preferred paths) and does not intend r(because it never occurs on S2)

28. Nov., 2008 ©Gao Yang, Ai Lab NJU 28 6.2 Cognitive Primitives

29. Nov., 2008 ©Gao Yang, Ai Lab NJU 29 6.2 Cognitive Primitives Some useful conclusion – IC1 Satisfiability This says that if p is intended by x, then it occurs eventually on some path. – IC2 Temporal Consistency This says that if an agent intends p and intends q, then it (implicitly) intends achieving them in some undetermined temporal order: p before q, q before p, or both simultaneously. – IC3 Persistence does not entail success Just because an agent persists with an intention does not mean that it will succeed.

30. Nov., 2008 ©Gao Yang, Ai Lab NJU 30 6.2 Cognitive Primitives 6.2.4 Commitments – Goals and intentions Are quite similar, and difference arises in their relationship with other modalities and how they evolve over time. Commitment can separate them. – Commitment Be treated as constraining how intentions are revised and updated. – Handling commitment IC4 shows how commitment may be expressed in the present framework.

31. Nov., 2008 ©Gao Yang, Ai Lab NJU 31 6.2 Cognitive Primitives – IC4 Persist while succeeding This constraint requires that agents desist from revising their intentions as long as they are able to proceed properly. If an agent selects some paths, then at future moments on those paths, it selects from among the future components of those paths.

32. Nov., 2008 ©Gao Yang, Ai Lab NJU 32 6.2 Cognitive Primitives 6.2.5 Know-how – Motivation Intentions have an obvious connection with actions – agents act to satisfy their intentions. But intentions do not ensure success. A key ingredient is know-how. – Example 6.7 Consider former figure, at t0, x may do either action a or action b, since both can potentially lead to one of the preferred paths being realized. However if the other agent does action d, then no matter which action x chooses, x will not succeed with its intentions, because none of its preferred paths will be realized.

33. Nov., 2008 ©Gao Yang, Ai Lab NJU 33 6.2 Cognitive Primitives – Let be the set of tree, and is defined as follows – SYN-19.

34. Nov., 2008 ©Gao Yang, Ai Lab NJU 34 6.2 Cognitive Primitives – SEM-32. – SEM-33. – SEM-36. – SEM-35.

35. Nov., 2008 ©Gao Yang, Ai Lab NJU 35 6.3 Belief Revision Beliefs – The bird caught in the trap is a swan – The bird caught in the trap comes from Sweden – Sweden is part of Europe – All European swans are white Consequences – The bird caught in the trap is white New information – The bird caught in the trap is black Which sentence would you give up?

36. Nov., 2008 ©Gao Yang, Ai Lab NJU 36 6.3.1 AGM Framework Alchourron, Gardenfors, and Makinson (1985) – Epistemic states: sets of formulas K. – Epistemic attitudes: - α accepted - α rejected Otherwise - α undetermined – Input: formula – Change operations: expansion, contraction, and revision

37. Nov., 2008 ©Gao Yang, Ai Lab NJU 37 6.3.1 AGM Framework Belief sets Three operations: – Expansion – Contraction – Revision (Levi identity) For contraction and revision, rationality postulates.

38. Nov., 2008 ©Gao Yang, Ai Lab NJU 38 6.3.1 AGM Framework Contraction Postulates

39. Nov., 2008 ©Gao Yang, Ai Lab NJU 39 6.3.1 AGM Framework Revision Postulates

40. Nov., 2008 ©Gao Yang, Ai Lab NJU 40 6.4 Social Primitives 6.6.1 Team and Organizational Structure

41. Nov., 2008 ©Gao Yang, Ai Lab NJU 41 6.4 Social Primitives 6.6.2 Mutual Beliefs and Joint Intentions

42. Nov., 2008 ©Gao Yang, Ai Lab NJU 42 6.4 Social Primitives 6.6.3 Social Commitments

43. Nov., 2008 ©Gao Yang, Ai Lab NJU 43 6.4 Social Primitives 6.6.4 Group Know-how and Intentions