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Formal Analysis of a Probabilistic Knowledge Communication Framework
Formal Analysis of a Probabilistic Knowledge Communication Framework João Carlos Gluz Rosa M. Vicari Cecília D. Flores Louise Seixas PIPCA/UNISINOS - RS - Brasil PPGC/PPGIE - UFRGS - RS - Brasil Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Overview
• • • • • • •
Research Questions Current Situation Approach to the Problem SLP Logic Probabilistic Communication Problem New Communicative Acts Formalization
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Research Questions Practical Considerations:
• How to model the communication of a Multiagent Intelligent Learning Environment in FIPA framework (AMPLIA learning environment)
• Agents rely on probabilistc knowledge (Bayesian Networks) inference and communication
•FIPA-ACL (or other ACLs) dos not provide facilities (methods) to communicate probabilistic knowledge (or represent it) that are consistent with the purely logical semantic of the ACL Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Research Questions Epistemological considerations:
• When agents reason using subjective (bayesian) probabilities they assign “degrees” (probabilities) to its beliefs
•When these agents need to communicate probabilistic beliefs they will try to assume that belief degrees are correctly communicated
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Research Questions Linguistic considerations: • In terms of illocutionary acts, this implies that the assertive force can have some kind of gradient ⇒ the degree of belief on the proposition
• Speech act theory does not assume that propositions of assertive acts must have some kind of internal structure
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Current Situation - agents logical reasoning No correlation between communication theories for
-agents probabilistic reasoning
• FIPA-ACL have an axiomatic semantic given by restricted versions of Speech Act Theory formalized in BDI models (Modal Logics) • Distributed BNs and MSBNs have algorithmic operational semantics directly based on the Theory of Probabilities Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Basic Approach
• Generalize the formal model used to give semantics to FIPAACL acts (the SL Logic) creating a new probabilistic modal logic => SLP logic
• Extend FIPA-ACL to support probabilistic assertive acts => inform-bp acts
• Allows the use of SLP as a content language
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
SLP Features
• Inherit all features of SL: first order modal logic with equality, modal operators for beliefs, choices, temporality and possibility. • Subjective (Belief) Probabilities given by probabilistic terms: BP(a,ϕ) ≥ 0 BP(a, ϕ ∨ ψ) = 1/2
• New constants, operations and variables over real numbers: (∀r)(r+1 ≥ r) (∃r)(r×r + (1+1)×r + (1+1+1) = 0)
• Probabilistic/Numerical Expressions: (∀r)(∀s)(BP(a, ϕ)=r ∧ BP(a, ϕ ∨ ψ)=s → s ≥ r) BP(a, ϕ ∨ ψ) = BP(a, ϕ) + BP(a, ψ)
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
SLP Properties
• Compatibility: Formulas valid in SL (theorems of SL) are also valid formulas of SLP • Soundness: SLP axiomatic system is proved sound
• Completeness: SLP axiomatic system is complete if the SL axiomatic system is also complete. Completeness depends on restrictions: All ϕ formulas contained in BP(a, ϕ) must be closed formulas (sentences) Numerical variables or constants are not allowed in logical terms and vice-versa
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Probabilistic Communication Principles
• Basic Assumption: agents that use FIPA-ACL to communicate probabilistic knowledge should respect the Agency and Communication Theories, which support FIPA standards.
• Probabilities and Beliefs Agreement: if some agent assumes that
the probability of proposition ϕ is p, then this is equivalent to state that it also believes in this fact: BP(a, ϕ)=p ↔ B(a, BP(a, ϕ)=p )
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Probabilistic Communication Principles
• Probabilities Adjustment: If any agent: believes the probability of ϕ is p, BP(a,ϕ)=p believes that it is competent about this belief, and B(a,Comp(a,BP(a,ϕ)=p))) believes that another agent estimates a different value for the probability of ϕ, BP(a,BP(b,ϕ)=p)New Communicative Acts: inform-bp: Informs the probability of closed formula ϕ. query-bp: Asks for the probability of closed formula ϕ. Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Formalization FP: BP(a,ϕ)=p ∧ BP(a, BP(b,ϕ)=p)
Formal Analysis of a Probabilistic Knowledge Communication Framework João Carlos Gluz Rosa M. Vicari Cecília D. Flores Louise Seixas PIPCA/UNISINOS - RS - Brasil PPGC/PPGIE - UFRGS - RS - Brasil Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Overview
• • • • • • •
Research Questions Current Situation Approach to the Problem SLP Logic Probabilistic Communication Problem New Communicative Acts Formalization
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Research Questions Practical Considerations:
• How to model the communication of a Multiagent Intelligent Learning Environment in FIPA framework (AMPLIA learning environment)
• Agents rely on probabilistc knowledge (Bayesian Networks) inference and communication
•FIPA-ACL (or other ACLs) dos not provide facilities (methods) to communicate probabilistic knowledge (or represent it) that are consistent with the purely logical semantic of the ACL Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Research Questions Epistemological considerations:
• When agents reason using subjective (bayesian) probabilities they assign “degrees” (probabilities) to its beliefs
•When these agents need to communicate probabilistic beliefs they will try to assume that belief degrees are correctly communicated
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Research Questions Linguistic considerations: • In terms of illocutionary acts, this implies that the assertive force can have some kind of gradient ⇒ the degree of belief on the proposition
• Speech act theory does not assume that propositions of assertive acts must have some kind of internal structure
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Current Situation - agents logical reasoning No correlation between communication theories for
-agents probabilistic reasoning
• FIPA-ACL have an axiomatic semantic given by restricted versions of Speech Act Theory formalized in BDI models (Modal Logics) • Distributed BNs and MSBNs have algorithmic operational semantics directly based on the Theory of Probabilities Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Basic Approach
• Generalize the formal model used to give semantics to FIPAACL acts (the SL Logic) creating a new probabilistic modal logic => SLP logic
• Extend FIPA-ACL to support probabilistic assertive acts => inform-bp acts
• Allows the use of SLP as a content language
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
SLP Features
• Inherit all features of SL: first order modal logic with equality, modal operators for beliefs, choices, temporality and possibility. • Subjective (Belief) Probabilities given by probabilistic terms: BP(a,ϕ) ≥ 0 BP(a, ϕ ∨ ψ) = 1/2
• New constants, operations and variables over real numbers: (∀r)(r+1 ≥ r) (∃r)(r×r + (1+1)×r + (1+1+1) = 0)
• Probabilistic/Numerical Expressions: (∀r)(∀s)(BP(a, ϕ)=r ∧ BP(a, ϕ ∨ ψ)=s → s ≥ r) BP(a, ϕ ∨ ψ) = BP(a, ϕ) + BP(a, ψ)
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
SLP Properties
• Compatibility: Formulas valid in SL (theorems of SL) are also valid formulas of SLP • Soundness: SLP axiomatic system is proved sound
• Completeness: SLP axiomatic system is complete if the SL axiomatic system is also complete. Completeness depends on restrictions: All ϕ formulas contained in BP(a, ϕ) must be closed formulas (sentences) Numerical variables or constants are not allowed in logical terms and vice-versa
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Probabilistic Communication Principles
• Basic Assumption: agents that use FIPA-ACL to communicate probabilistic knowledge should respect the Agency and Communication Theories, which support FIPA standards.
• Probabilities and Beliefs Agreement: if some agent assumes that
the probability of proposition ϕ is p, then this is equivalent to state that it also believes in this fact: BP(a, ϕ)=p ↔ B(a, BP(a, ϕ)=p )
Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Probabilistic Communication Principles
• Probabilities Adjustment: If any agent: believes the probability of ϕ is p, BP(a,ϕ)=p believes that it is competent about this belief, and B(a,Comp(a,BP(a,ϕ)=p))) believes that another agent estimates a different value for the probability of ϕ, BP(a,BP(b,ϕ)=p)New Communicative Acts: inform-bp: Informs the probability of closed formula ϕ. query-bp: Asks for the probability of closed formula ϕ. Gluz, Vicari, Flores & Seixas
october, 2006
Formal Analysis of a Probabilistic Knowledge Communication Framework
Formalization FP: BP(a,ϕ)=p ∧ BP(a, BP(b,ϕ)=p)
