Modeling Speech Acts and Joint Intentions in Modal Markov Logic

Henry Kautz

University of Washington

Goal Unified way to specify and reason about

Communicative actions Domain specific actions Joint and individual obligations Beliefs of agents about other agents

Criteria Handle uncertain and incomplete knowledge Support well-founded and efficient inference Support learning

Markov Logic Language for statistical-relational learning

Developed by Pedro Domingos [2004+] Clausal (CNF) syntax

Clauses may be hard or soft Weights of soft clauses are learned from examples

Semantics: compilation to a Markov model

Example

Advantages of Markov Logic

Expressive power of (finite domain) first-order logic Ontologies: project_review(x) => meeting(x) Relations: manages(Bill,CALO) Rules:

manages(x,y) & DARPA_project(y) => has_headache(x) Dynamic worlds: at(A,L1,i) & go(L1,L2,i,j) => at(A,L2,j)

Supports both weight and structure learning Very efficient local-search algorithms for computing

most likely assignment (MPE) Language of CALO Probabilistic Consistency

Engine (Uribe & Dietterich)

What’s Missing?

Consider representing the felicity conditions for the speech act Ask_If(S,H,P): Preconditions:

Speaker does not know whether P holds Speaker wants to know whether P holds Speaker believes Hearer knows whether P holds

Effects Hearer believes Speaker wants to know whether P holds

Modal Logic

Logics for representing attitudes such as Knows, Believes, Wants, Ought, …

Traditionally formalized by rules & axiom schemas, e.g.: If p can be deduced, then Bp (necessitation) B(p => q) => (Bp => Bq) (distribution) Bp => BBp (introspection) …

Issues in Adding Modalities to Markov Logic

ML is not a deductive system: consequences follow from probabilistic semantics There cannot be an explicit rule of necessitation;

instead, must follow from probabilistic semantics ML only defined for finite structures

Distribution (and other axiom schemas) must not require infinite instantiations

Modal Markov Logic Ba

Ba P means agent a believes P Need not be certain belief Intuitively: the agent’s belief is actionable

Syntax KB = conjunction of weighted clauses Clause = disjunction of literals Literal = Atom or ~Atom Atom = Proposition or Ba(Clause) Extend to quantification over sets of constant

terms

Inference

Given a KB and a query, construct a Markov graph with Nodes for each (ground) atom and its negation Weighted hyperedges for each top-level clause Unweighted (strict) hyperedges connecting each

modal atom to the atoms for its disjuncts, and to the negations of its disjuncts Enforce consistency Enforce distribution

Example

B(p v q)

B p B q B ~qB ~p

B~p & B(p v q) => Bq

~B~p v ~Bp ~B~q v ~Bq

B~q & B(p v q) => Bp

Uses of soft rules: speech acts

Practically all preconditions and effects of communication acts are non-categorical E.g.: you may ask a question whose answer you

already know the answer Exceptions (and exceptions to exceptions…) need

not be explicitly written into each rule Higher-weighted rules can over-rule lower weighted

rules Can learn weights (& rules!) corresponding to different

styles of discourse

Uses of soft rules: joint obligations

Let M(a,b,g,i) = at time i, agent a is obliged to agent b to perform g

Simple soft persistence axiom: M(a,b,g,i) => does(a,g) v M(a,b,g,i+1) A purely logical persistence rule for obligations

would be extremely complex Such complexities (what if b dies? what is g

becomes impossible? etc) can be added as needed as additional soft rules

Uses of soft rules: plan recognition & cooperative behavior

Let W(a,p) = agent a wants p Cooperative agents

Try to recognize the goals of other agents

W(a,p) & enables(p,q) => W(a,q) Adopt those goals as their own (under proper

circumstances)

B(a,W(b,g)) & cooperative(a,b) => W(a,g)

Status 2nd generation (non-modal) UW Markov Logic

engine has been released Working on proofs of soundness & completeness of

modal extension Next steps

Implement Markov graph instantiation routines for modalities

Hand-code speech act, obligation persistence, and (simple) plan-recognition rules

Create or find annotated discourse transcripts and use to train weights Extend SRI/ICSI annotated corpus to include annotations

about agents’ mental state, as well as dialogs acts