DERI Research Seminar

1. DERI Research Seminar „Some philosophical problems from the standpoint of artificial intelligence“ – John McCarthy & Patrick J. Hayes, 1969 Uwe Keller

2. Overview • Motivation • Philosophical questions • Formalisms: Situation Calculus • Remarks & open problems • Discussion of literature DERI Research Seminar 03/2004

3. Motivation • A dream of CS researchers: Intelligent Agents • Requires … • General representationof the world in terms of which the inputs are interpreted • Commitment on: what is knowledge and how is it obtained? ► Some of the major traditional problems of philosophy arise in AI too! • More specifically: We want to build a program that … • decides what to do by inferring in a formal language that a certain strategy will achieve its assigned goal. ► Hence, we have to formalize the notions • causality (“causes”), ability (“can”) and knowledge (“knows”). DERI Research Seminar 03/2004

4. … Philosophical questions Adequate representation of the world „can“, „causes“, „knows“

5. Representation of the world • We have to decide … • What structure is the world to be regarded as having • How to represent information about … • the world & its laws of change in the machine • Adequacy of such a representation ? Def.: A representation is metaphysically adequate if the world could have that form without contradicting the facts of the aspect of reality that interests us. • Examples (for different aspects of reality) … • Representation of the world as a collection of particles interacting through forces between each pair of particles • Representation of the world as a giant quantum-mechanical wave function • Representation as a system of interacting discrete automata DERI Research Seminar 03/2004

6. Representation of the world (II) Def.: A representation is epistemologically adequate for a person or machine if it can used be practically to express the facts that one actually has about the world. ►None of the given examples are adequate for representing e.g. „John is at home“ or „dogs chase cats“! • Ordinary language … • is obviously adequate to express facts that people communicate to each other in ordinary language, but … • is not adequate e.g. for expressing what people know about how to recognize a particular face. • Later: • Give an epistemologically adequate formal representation of common-sense facts for causality, ability and knowledge DERI Research Seminar 03/2004

7. Automaton representation Let S be a system of interacting discrete finite automata: S = (Subautomata, Signals, Statefunctions, Outputfunctions) • Statefunction: ai(t+1) = Ai(ai(t), s1(t), …, sk(t)), t=0,1, … (time) • Outputfunction: si(t+1) = Si(ai(t)) • Input/Output of S are defined as expected • Simplest examples of systems that interact over time; determ. • Automaton representation: Consider the world as such an S • Difficulties with this model in some situations: • Huge number of states, e.g. representing all the knowledge of a person • Geometric info about objects are hard to represent • System of fixed interconnections is inadequate • Most serious objection: Not epistemologically adequate: We don‘t ever know a person well enough to list all his internal states. The kind of information we do have about him has to be represented in some other way („know“) • But: We may use it for concepts of „can“, „causes“ and „believes“ DERI Research Seminar 03/2004

8. Notion of „can“ • Let S be a system of automata (SOA) without external inputs, p be a subautomata with m output signals. • Let S* be the SOA which is obtained by disconnecting these m signals from p and replacing them by external input lines • Then • The new system S* has always the same set of states as S • Let πbe a condition on the state - „the box is under the bananas“ • We‘ll write can(p,π,s) („subautomaton p can bring about the condition π in state s“) … • if there is a sequence of outputs of S* which that will eventually put S into a state a‘ that satisfies π(a‘) • In other words: In determining what p can achieve, we consider the effects of sequences of ist actions, quite apart form the conditions what it actually will do! • This seems to be in line with our common-sense notion of „can“ • But needs further elaboration for actual coverage of common-sense notion and for practical purposes! DERI Research Seminar 03/2004

9. Notion of „can“ (II) • Now suppose that S admits external inputs. • Then, there are two possible definitions of „can“: • Assert that can(p,π,s) if p can achieve πregardless of what signals appear on external inputs („cana“) • Note, that we‘re not requiring here that p have any way of knowing what the external inputs were • p can achieve a goal if the goal would be achieved for arbitrary inputs by some automaton put in place of p („canb“) • Counter-intuitive, since „can“ only depends on the place instead of the function of automaton p DERI Research Seminar 03/2004

10. Notion of „causes“ • Besides the explication of „can“, the automata representation of the world is very suited for defining notions of causalty: • causes(p,π,s) = subautomaton p caused the condition πin s • causes(p,π,s) if changing the output of p would prevent π. DERI Research Seminar 03/2004

11. … Formalisms for proving that a strategy will achieve a goal Situation, fluent, future operator action, strategy, result of a strategy & knowledge

12. Situation • Definition • A situation s is the complete state of the universe at an instant of time. • Sit := {s | s is situation} • Since the universe is too large, we‘ll never describe the universe completely, but give only facts • These facts will be used to deduce further facts about that situation, future situations, situations that persons can bring about • Requires also to consider hypothetical situations • These situations can‘t be completely described, but with sufficient details for some purposes. (Jones-sell-car) DERI Research Seminar 03/2004

13. Fluents • Idea: Partial description of a situation s • Definition • A fluent f is a function with domain Sit • Range of f • {true,false}: propositional fluent • Sit: situational fluent • Fluents are often the values of functions • raining(x) is a fluent f s.t. raining(x)(s) is true iff. it is raining at the place x in situation s • Also written as: raining(x,s), … DERI Research Seminar 03/2004

14. Causality • Make assumptions about causality by means of a fluent F(π) (where π is a fluent itself!) • F(π,s) asserts that the situation s will be followed (after some time) by a situation that satisfies the fluent π • Example: • All x, All p [ raining(x) and at(p,x) and outside(x) -> F(wet(p))] • Expression of physical laws, … • Other useful operators • F(π,s): For some situation s‘ in the future of s holds π(s‘) • G(π,s): For all situation s‘ in the future of s holds π(s‘) • P(π,s): For some situation s‘ in the past of s holds π(s‘) • H(π,s): For all situation s‘ in the past of s holds π(s‘) DERI Research Seminar 03/2004

15. Causality (II) • It seems also useful to to define the situational fluent next(π) • The next situation s‘ in the future of s for which π(s‘) holds • If there is no such fluent (not F(π,s)) then next(π) is undefined DERI Research Seminar 03/2004

16. Actions • Fundamental role in our study of actions: • Situational fluent: result(p,σ, s) where … • p:Person, σ: Action/Strategy, s:Situation • The value of result(p,σ, s) is the situation that results when p carries out σ, starting in situation s • When σ is nonterminating in that context, this value is undefined • With this fluent, we can express certain laws of ability: • e.g.: has(p,k,s) and fits(k,sf) and at(p,sf,s) -> open(sf, result(p,open(sf,k)),s)) DERI Research Seminar 03/2004

17. Strategies • Actions can be combined into strategies • Simplest case: Finite sequence of actions • More general: ALGOL-like compound statement • containing actions written in the form of procedure calling assignement statements and conditional GOTO statements • Example strategy: begin face(South) n:=0; b: if n = 17 then goto a; walk-a-block;n:=n+1; goto b; a: turn-right; c: walk-a-block; if name-on-street-sign <> ‚Chestnut Street‘ then goto c; end; DERI Research Seminar 03/2004

18. Strategies applied (I) • In order to apply mathematical theory of computation (Manna) • Write program differently: replace each occurrence of an action A by an assignement statement „s:=result(p,A,s)“ • For our example strategy this means … • Try to show: John can go home, provided that he initially is in his office begin s:= result(p, face(South), s); n:=0; b: if n = 17 then goto a; s:=result(p,walk-a-block,s);n:=n+1; goto b; a: s:=result(p,turn-right,s); c: s:=result(p,walk-a-block,s); if name-on-street-sign <> ‚Chestnut Street‘ then goto c; end; DERI Research Seminar 03/2004

19. Strategies applied (II) Ex s0 ( at(John, office(John), s0) and q1(0, result(John, face(South),s0)) ) -> Ex n,s ( q1(n,s) and if n = 17 then q2(result(John, walk-a-block, result(John,turn-right,s))) else not q1(n+1, result(John, walk-a-block, s))) or Ex s ( q2(s) and if name-on-street-sign <> ‚Chestnut Street‘ then not q2(result(John,walk-a-block, s)) else at(John, home(John), s)) • Given • initial condition: at(John, office(John), s0) • final condition: at(John, home(John), s) • and our strategy (program) S • The Theory of Manna allows us to generate a sentence W of FOL • Proving W will show that S terminates and that when it terminates s will satisfy at(John, home(John), s) begin s:= result(p, face(South), s); n:=0; b: if n = 17 then goto a; s:=result(p,walk-a-block,s);n:=n+1; goto b; a: s:=result(p,turn-right,s); c: s:=result(p,walk-a-block,s); if name-on-street-sign <> ‚Chestnut Street‘ then goto c; end; DERI Research Seminar 03/2004

20. Strategies applied (III) • Needed facts for proving W • Facts of geography • Fluent „name-on-street-sign“ will have the value ‚ChS‘ at that point • Facts giving the effects of action A expressed as predicates about result(p,A,s) deducible from sentences about s • Axiomschema for induction Ex s0 ( at(John, office(John), s0) and q1(0, result(John, face(South),s0)) ) -> Ex n,s ( q1(n,s) and if n = 17 then q2(result(John, walk-a-block, result(John,turn-right,s))) else not q1(n+1, result(John, walk-a-block, s))) or Ex s ( q2(s) and if name-on-street-sign <> ‚Chestnut Street‘ then not q2(result(John,walk-a-block, s)) else at(John, home(John), s)) DERI Research Seminar 03/2004

21. … Remarks & open problems in extenting the discussed formalism

22. result(p,o,s) … • Approximate character of result(p,o,s) • Using the situational fluent result(p,o,s) has 2 main advantages over the can(p,π,s) from section 2: • permits more compact and transparent sentences • lends itself to the application of the mathematical theory of computation • However • it‘s only an approximation to say that an action (other than that which will actually occur) leads to a definite situation (Spontaneous, emotional decision on actions in the real-world vs. artifical operations under partial knowledge) DERI Research Seminar 03/2004

23. Possible meanings for „can“ • A computer program can readily be given much more powerful introspection than a person has (self-simulation possible!) • Various possible notions of „can(Program, Cond)“ for a computer program: • The is a subprogram S and room for it in the memory which would achieve Cond if it where in the memory and control were transfered to S. No assertion is made that Program knows S or even knows that S exists • S exists as above and that S will achieve Cond follows from information in memory according to a proof that Program is capable of checking • Program‘s standard problem-solving procedure will find S if achieving Cond is ever accepted as a subgoal DERI Research Seminar 03/2004

24. Frame Problem • As often for formalisms that „hypothetically“ execute State-Transitions: • What changes and what stays unchanged? • Explicit unchanged statements might be needed to proof something. This can be a tedious task DERI Research Seminar 03/2004

25. Questions ?