Modeling Speech Acts and
Joint Intentions in Modal
Markov Logic
Henry Kautz
University of Washington
Goal
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Unified way to specify and reason about
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Communicative actions
Domain specific actions
Joint and individual obligations
Beliefs of agents about other agents
Criteria
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Handle uncertain and incomplete knowledge
Support well-founded and efficient inference
Support learning
Markov Logic
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Language for statistical-relational learning
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Developed by Pedro Domingos [2004+]
Clausal (CNF) syntax
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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
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Expressive power of (finite domain) first-order logic
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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?
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Consider representing the felicity conditions
for the speech act Ask_If(S,H,P):
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Preconditions:
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Speaker does not know whether P holds
Speaker wants to know whether P holds
Speaker believes Hearer knows whether P holds
Effects
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Hearer believes Speaker wants to know whether P holds
Modal Logic
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Logics for representing attitudes such as
Knows, Believes, Wants, Ought, …
Traditionally formalized by rules & axiom
schemas, e.g.:
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If p can be deduced, then Bp (necessitation)
B(p => q) => (Bp => Bq)
(distribution)
Bp => BBp
(introspection)
…
Issues in Adding Modalities to
Markov Logic
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ML is not a deductive system: consequences
follow from probabilistic semantics
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There cannot be an explicit rule of necessitation;
instead, must follow from probabilistic semantics
ML only defined for finite structures
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Distribution (and other axiom schemas) must not
require infinite instantiations
Modal Markov Logic Ba
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Ba P means agent a believes P
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Need not be certain belief
Intuitively: the agent’s belief is actionable
Syntax
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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
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Given a KB and a query, construct a Markov
graph with
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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
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Enforce consistency
Enforce distribution
Example
~B~p v ~Bp
B ~p
~B~q v ~Bq
Bp
Bq
B~p & B(p v q) => Bq
B ~q
B~q & B(p v q) => Bp
B(p v q)
Uses of soft rules: speech acts
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Practically all preconditions and effects of
communication acts are non-categorical
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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
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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
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Let M(a,b,g,i) = at time i, agent a is obliged to
agent b to perform g
Simple soft persistence axiom:
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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
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Let W(a,p) = agent a wants p
Cooperative agents
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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
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2nd generation (non-modal) UW Markov Logic
engine has been released
Working on proofs of soundness & completeness of
modal extension
Next steps
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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
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Extend SRI/ICSI annotated corpus to include annotations
about agents’ mental state, as well as dialogs acts