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 pB qB ~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 2 nd 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