Means-end Relations and a Measure of Efficacy Jesse Hughes 1 Albert - PowerPoint PPT Presentation

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Functional ascriptions “The function of the heart is to pump blood.” “That switch mutes the television.” “The subroutine ensures that the user is authorized.” “The magician’s assistant is for distracting the audience.” Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Functional ascriptions “The function of the heart is to pump blood.” “That switch mutes the television.” “The subroutine ensures that the user is authorized.” “The magician’s assistant is for distracting the audience.” We ascribe functions to biological stuff, Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Functional ascriptions “The function of the heart is to pump blood.” “That switch mutes the television.” “The subroutine ensures that the user is authorized.” “The magician’s assistant is for distracting the audience.” We ascribe functions to biological stuff, artifacts, Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Functional ascriptions “The function of the heart is to pump blood.” “That switch mutes the television.” “The subroutine ensures that the user is authorized.” “The magician’s assistant is for distracting the audience.” We ascribe functions to biological stuff, artifacts, algorithms, Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Functional ascriptions “The function of the heart is to pump blood.” “That switch mutes the television.” “The subroutine ensures that the user is authorized.” “The magician’s assistant is for distracting the audience.” We ascribe functions to biological stuff, artifacts, algorithms, personal roles. . . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” ⇓ One can use the switch to mute the television. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” ⇓ One can use the switch to mute the television. ⇓ Some action involving the switch will cause the television to be muted. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” ⇓ One can use the switch to mute the television. ⇓ Some action involving the switch will cause the television to be muted. Functions imply means-end relations. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” ⇓ One can use the switch to mute the television. ⇓ Some action involving the switch will cause the television to be muted. Functions imply means-end relations. Doesn’t imply desirability of the end. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” ⇓ One can use the switch to mute the television. ⇓ Some action involving the switch will cause the television to be muted. Functions imply means-end relations. Doesn’t imply desirability of the end. Needed: means-end semantics distinct of desirability Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic How functions relate to means and ends “That switch mutes the television.” ⇓ One can use the switch to mute the television. ⇓ Some action involving the switch will cause the television to be muted. Functions imply means-end relations. Doesn’t imply desirability of the end. Needed: means-end semantics distinct of desirability distinct from theory of practical reasoning Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Initial analysis of means-end relations An end is some desirable condition – a proposition . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Initial analysis of means-end relations An end is some desirable condition – a proposition . A means is a way of making the end true. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Initial analysis of means-end relations An end is some desirable condition – a proposition . A means is a way of making the end true. Means change things: means are actions . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Initial analysis of means-end relations An end is some desirable condition – a proposition . A means is a way of making the end true. Means change things: means are actions . Some controversies: Ends-in-themselves? Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Initial analysis of means-end relations An end is some desirable condition – a proposition . A means is a way of making the end true. Means change things: means are actions . Some controversies: Ends-in-themselves? Objects as means? Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Basic types: a set act of actions , Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Basic types: a set act of actions , Closed under: sequential composition α ; β non-deterministic choice α ∪ β test ϕ ? iteration α ∗ Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Basic types: a set act of actions , Closed under: sequential composition α ; β non-deterministic choice α ∪ β test ϕ ? iteration α ∗ a set prop of propositions . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Basic types: a set act of actions , Closed under: sequential composition α ; β non-deterministic choice α ∪ β test ϕ ? iteration α ∗ a set prop of propositions . Closed under: boolean connectives, dynamic operators [ α ] ϕ , � α � ϕ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Basic types: a set act of actions , Closed under: sequential composition α ; β non-deterministic choice α ∪ β test ϕ ? iteration α ∗ a set prop of propositions . Closed under: boolean connectives, dynamic operators [ α ] ϕ , � α � ϕ . Intuitions: [ α ] ϕ : after doing α , ϕ will hold. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL syntax Propositional Dynamic Logic is a logic of actions. Basic types: a set act of actions , Closed under: sequential composition α ; β non-deterministic choice α ∪ β test ϕ ? iteration α ∗ a set prop of propositions . Closed under: boolean connectives, dynamic operators [ α ] ϕ , � α � ϕ . Intuitions: [ α ] ϕ : after doing α , ϕ will hold. � α � ϕ : after doing α , ϕ might hold. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL semantics Possible world semantics with transition systems for each action α . α α α α Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL semantics Possible world semantics with transition systems for each action α . α α � w ′ means: w α one can reach w ′ by doing α in w . α α Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL semantics Possible world semantics with transition systems for each action α . α α � w ′ means: P w α one can reach w ′ by doing α in w . α P α ] α [ � w ′ . w ′ | α = [ α ] ϕ iff ∀ w w | = ϕ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic PDL semantics Possible world semantics with transition systems for each action α . α � w ′ means: w β Q one can reach w ′ by doing α in w . β Q � β β � � w ′ . w ′ | α = [ α ] ϕ iff ∀ w w | = ϕ . � w ′ . w ′ | α w | = � α � ϕ iff ∃ w = ϕ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Weak and strong means-end relations A means is an action α that can realize one’s end ϕ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Weak and strong means-end relations A means is an action α that can realize one’s end ϕ . Two interpretations: α α ϕ Weak: α might realize ϕ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Weak and strong means-end relations A means is an action α that can realize one’s end ϕ . Two interpretations: α α α α ϕ ϕ Weak: α might realize ϕ . Strong: α will realize ϕ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Weak and strong means-end relations A means is an action α that can realize one’s end ϕ . Two interpretations: α α α α ϕ ϕ Weak: α might realize ϕ . Strong: α will realize ϕ . w | = � α � ϕ w | = [ α ] ϕ ∧ � α �⊤ Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Interest I: Practical syllogisms Means-end relations Interest II: Functional ascriptions Efficacy via fuzzy logic Propositional Dynamic Logic Weak and strong means-end relations A means is an action α that can realize one’s end ϕ . Two interpretations: α α α α ϕ ϕ Weak: α might realize ϕ . Strong: α will realize ϕ . w | = � α � ϕ w | = [ α ] ϕ ∧ � α �⊤ � �� � α can be done. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Outline Means-end relations 1 Interest I: Practical syllogisms Interest II: Functional ascriptions Propositional Dynamic Logic Efficacy via fuzzy logic 2 Reliability as a fuzzy operator The resulting fuzzy logic Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Means distinguished by efficacy Different means to a common end have different degrees of reliability. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Means distinguished by efficacy Different means to a common end have different degrees of reliability. End: Get 12 points with one dart. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Means distinguished by efficacy Different means to a common end have different degrees of reliability. End: Get 12 points with one dart. Three different means: Throw for 12. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Means distinguished by efficacy Different means to a common end have different degrees of reliability. End: Get 12 points with one dart. Three different means: Throw for 12. Throw for double 6. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Means distinguished by efficacy Different means to a common end have different degrees of reliability. End: Get 12 points with one dart. Three different means: Throw for 12. Throw for double 6. Throw for triple 4. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Means distinguished by efficacy Different means to a common end have different degrees of reliability. End: Get 12 points with one dart. Three different means: Throw for 12. Throw for double 6. Throw for triple 4. Efficacy: The degree of reliability of a means to an end. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Efficacy is a measure of likelihoods. α α Q β β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Efficacy is a measure of likelihoods. α PDL includes non-determinism, α not probabilities. Q β β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Efficacy is a measure of likelihoods. α PDL includes non-determinism, , 0 . 2 α not probabilities. Q 0 . 8 Fix (semantic): use 0 . 1 probabilistic transition structures. β 9 . 0 , β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Efficacy is a measure of likelihoods. α PDL includes non-determinism, , 0 . 2 α not probabilities. Q 0 . 8 Fix (semantic): use 0 . 1 probabilistic transition structures. β 9 . 0 , β α � w ′ means that w x doing α in w has probability x of resulting in w ′ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Efficacy is a measure of likelihoods. α PDL includes non-determinism, , 0 . 2 α not probabilities. Q 0 . 8 Fix (semantic): use 0 . 1 probabilistic transition structures. β 9 . 0 , β α � w ′ means that w x doing α in w has probability x of resulting in w ′ . α � w ′ ) = x . Write: P ( w Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? α , 0 . 2 α Q 0 . 8 0 . 1 β 9 . 0 , β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 0 . 1 β 9 . 0 , β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 β 9 . 0 , β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 Nesting requires picking x ’s. β 9 . 0 , β Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 Nesting requires picking x ’s. β 9 . 0 , β Probabilistic PDL? Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 Nesting requires picking x ’s. β 9 . 0 , β Probabilistic PDL? Truth functional. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 Nesting requires picking x ’s. β 9 . 0 , β Probabilistic PDL? Truth functional. Assigns values in [0 , 1] to world-formula pairs. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 Nesting requires picking x ’s. β 9 . 0 , β Probabilistic PDL? Truth functional. Assigns values in [0 , 1] to world-formula pairs. Logic in loose sense. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic From non-determinism to probabilities Syntactic fix? Probabilistic Computation Tree α , 0 . Logic (pCTL)? 2 α Q 0 . 8 Index dynamic operators, like [ α ] ≥ x , � α � ≥ x . 0 . 1 Nesting requires picking x ’s. β 9 . 0 , β Probabilistic PDL? Truth functional. Assigns values in [0 , 1] to world-formula pairs. Logic in loose sense. Fuzzy PDL. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic But probability � = fuzziness. . . Slogan: Probabilities and fuzziness are different. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic But probability � = fuzziness. . . Slogan: Probabilities and fuzziness are different. But one can use probabilities to define fuzzy predicates. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic But probability � = fuzziness. . . Slogan: Probabilities and fuzziness are different. But one can use probabilities to define fuzzy predicates. Hajek, et al., uses distributions on propositional formulas to define “Probably ϕ ”. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic But probability � = fuzziness. . . Slogan: Probabilities and fuzziness are different. But one can use probabilities to define fuzzy predicates. Hajek, et al., uses distributions on propositional formulas to define “Probably ϕ ”. Truth degree of “Probably ϕ ” = P ( ϕ ) . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. α Q α Q α � α � Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ Q α Q α � α � Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ 0 . 5 Q α In fuzzy PDL: 0 . 5 Q α � � α � ϕ ⇔ α will probably realize ϕ α 1 � Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ 0 . 5 Q α In fuzzy PDL: 0 . 5 Q α � � α � ϕ ⇔ α will probably realize ϕ α 1 � ⇔ α reliably realizes ϕ Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ 0 . 5 Q α In fuzzy PDL: 0 . 5 Q α � � α � ϕ ⇔ α will probably realize ϕ α 1 � ⇔ α reliably realizes ϕ � α → w ′ ) · � ϕ � ( w ′ ) . � � α � ϕ � ( w ) = P ( w − w ′ ∈W Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ 0 . 5 Q α In fuzzy PDL: 0 . 5 Q α � � α � ϕ ⇔ α will probably realize ϕ α 1 � ⇔ α reliably realizes ϕ � α → w ′ ) · � ϕ � ( w ′ ) . � � α � ϕ � ( w ) = P ( w − w ′ ∈W Like decision theory, we use means for expected outcomes. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ 0 . 5 Q α In fuzzy PDL: 0 . 5 Q α � � α � ϕ ⇔ α will probably realize ϕ α 1 � ⇔ α reliably realizes ϕ � α → w ′ ) · � ϕ � ( w ′ ) . � � α � ϕ � ( w ) = P ( w − w ′ ∈W Like decision theory, we use means for expected outcomes. Unlike decision theory, there are no utilities involved. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Reliability as a fuzzy proposition “Reliably”, like “Probably”, is a vague operator. In PDL: α � α � ϕ ⇔ α will possibly realize ϕ 0 . 5 Q α In fuzzy PDL: 0 . 5 Q α � � α � ϕ ⇔ α will probably realize ϕ α 1 � ⇔ α reliably realizes ϕ � α → w ′ ) · � ϕ � ( w ′ ) . � � α � ϕ � ( w ) = P ( w − w ′ ∈W Like decision theory, we use means for expected outcomes. Unlike decision theory, there are no utilities involved. Elegant treatment of complex ends, like � α � ϕ ∧ � β � ψ . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Fuzzy ends An accidental advantage Weapons are for causing harm. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Fuzzy ends An accidental advantage Weapons are for causing harm. Examples: slingshot, nuke Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Fuzzy ends An accidental advantage Weapons are for causing harm. Examples: slingshot, nuke This end is fuzzy. m r a H Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Fuzzy ends An accidental advantage Weapons are for causing harm. Examples: slingshot, nuke This end is fuzzy. Fuzzy PDL allows for fuzzy ends. m n u r k a e H 1 A nuke is more effective in sling causing harm than a slingshot. 0 . 5 g n (Duh.) i l s 5 . 0 Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. J knows that L will either do m in order to realize P or Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. J knows that L will either do m in order to realize P or n in order to realize Q . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. J knows that L will either do m in order to realize P or n in order to realize Q . He wants to ensure that L will succeed, whichever she chooses. Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. J knows that L will either do m in order to realize P or n in order to realize Q . He wants to ensure that L will succeed, whichever she chooses. End : � m � P ∧ � n � Q . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. J knows that L will either do m in order to realize P or n in order to realize Q . He wants to ensure that L will succeed, whichever she chooses. End : � m � P ∧ � n � Q . Aim : maximize min { � � m � P � ( w ) , � � n � Q � ( w ) } . Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy

Means-end relations Reliability as a fuzzy operator Efficacy via fuzzy logic The resulting fuzzy logic Extending the logic to other connectives Suppose J and L are cooperative but incommunicado. J knows that L will either do m in order to realize P or n in order to realize Q . He wants to ensure that L will succeed, whichever she chooses. End : � m � P ∧ � n � Q . Aim : maximize min { � � m � P � ( w ) , � � n � Q � ( w ) } . � � � ϕ ∧ ψ � ( w ) = min � ϕ � ( w ) , � ψ � ( w ) Hughes, Esterline, Kimiaghalam Means-end Relations and a Measure of Efficacy