Simple Hyperintensional Belief Revision Franz Berto F.Berto@uva.nl Bochum, 15-16 Dec 2017
1. Intro Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 2 / 34
1. Intro In [Alchourrón et al., 1985] (K*1) has K ∗ φ closed under full classical logic. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 3 / 34
1. Intro In [Alchourrón et al., 1985] (K*1) has K ∗ φ closed under full classical logic. But, our belief states needn’t be closed under classical logic – perhaps under any kind of monotonic consequence [Jago, 2014]. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 3 / 34
1. Intro In [Alchourrón et al., 1985] (K*1) has K ∗ φ closed under full classical logic. But, our belief states needn’t be closed under classical logic – perhaps under any kind of monotonic consequence [Jago, 2014]. (K*5) trivializes belief sets revised in the light of inconsistent information. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 3 / 34
1. Intro In [Alchourrón et al., 1985] (K*1) has K ∗ φ closed under full classical logic. But, our belief states needn’t be closed under classical logic – perhaps under any kind of monotonic consequence [Jago, 2014]. (K*5) trivializes belief sets revised in the light of inconsistent information. But, we shouldn’t go crazy after occasional exposure to inconsistent info. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 3 / 34
1. Intro In [Alchourrón et al., 1985] (K*1) has K ∗ φ closed under full classical logic. But, our belief states needn’t be closed under classical logic – perhaps under any kind of monotonic consequence [Jago, 2014]. (K*5) trivializes belief sets revised in the light of inconsistent information. But, we shouldn’t go crazy after occasional exposure to inconsistent info. (K*6) has it that, if φ and ψ are logically equivalent, then K ∗ φ = K ∗ ψ . Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 3 / 34
1. Intro In [Alchourrón et al., 1985] (K*1) has K ∗ φ closed under full classical logic. But, our belief states needn’t be closed under classical logic – perhaps under any kind of monotonic consequence [Jago, 2014]. (K*5) trivializes belief sets revised in the light of inconsistent information. But, we shouldn’t go crazy after occasional exposure to inconsistent info. (K*6) has it that, if φ and ψ are logically equivalent, then K ∗ φ = K ∗ ψ . But, we are subject to framing effects [Kahneman and Tversky, 1984]: Lois may revise her beliefs one way when told she has 60% chances of succeeding in a task, another way when told she has has 40% chances of failing. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 3 / 34
1. Intro Lots of doxep logics include operators for conditional belief, B φ ψ (‘Condi- tional on φ , it is believed that ψ ’, or ‘It is believed that ψ after receiving the information that φ ’), or dynamic belief revision, [ ∗ φ ] B ψ (‘After revision by φ , it is believed that ψ ’), closely mirroring the original AGM postulates. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 4 / 34
1. Intro Lots of doxep logics include operators for conditional belief, B φ ψ (‘Condi- tional on φ , it is believed that ψ ’, or ‘It is believed that ψ after receiving the information that φ ’), or dynamic belief revision, [ ∗ φ ] B ψ (‘After revision by φ , it is believed that ψ ’), closely mirroring the original AGM postulates. E.g., [Spohn, 1988], [Segerberg, 1995], [Lindström and Rabinowicz, 1999], [Board, 2004], [Van Ditmarsch, 2005], [Asheim and Sövik, 2005], [Leitgeb and [van Benthem, 2007], [van Ditmarsch et al., 2007], [Baltag and Smets, 2008], [van Benthem, 2011], [Girard and Rott, 2014] Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 4 / 34
1. Intro E.g. as for (K*6), such logics will typically satisfy: If � φ ↔ ψ , then � [ ∗ φ ] χ ↔ [ ∗ ψ ] χ If � φ ↔ ψ , then � B φ χ ↔ B ψ χ Logically equivalent φ and ψ can be replaced salva veritate as indexes in [ ∗ ... ] and B ... : these can’t detect hyperintensional differences. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 5 / 34
1. Intro E.g. as for (K*6), such logics will typically satisfy: If � φ ↔ ψ , then � [ ∗ φ ] χ ↔ [ ∗ ψ ] χ If � φ ↔ ψ , then � B φ χ ↔ B ψ χ Logically equivalent φ and ψ can be replaced salva veritate as indexes in [ ∗ ... ] and B ... : these can’t detect hyperintensional differences. But, thought is hyperintensional (framing is just a special case): Lois can wish that Superman is in love with her without wishing that Clark Kent is in love with her. We can conceive that 75 × 12 = 900 without conceiving that Fermat’s Last Theorem is true. Etc. etc. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 5 / 34
1. Intro In this work, I want to model an agent: whose belief revision processes are sensitive to framing effects; Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 6 / 34
1. Intro In this work, I want to model an agent: whose belief revision processes are sensitive to framing effects; who can hold inconsistent beliefs without thereby believing everything; Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 6 / 34
1. Intro In this work, I want to model an agent: whose belief revision processes are sensitive to framing effects; who can hold inconsistent beliefs without thereby believing everything; who is safe from various other forms of logical omniscience. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 6 / 34
1. Intro Start from a single, plain insight: we should take at face value the view of beliefs as (propositional) representational mental states bearing intentional- ity , that is, being about states of affairs, situations, or circumstances which make for their content. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 7 / 34
1. Intro Start from a single, plain insight: we should take at face value the view of beliefs as (propositional) representational mental states bearing intentional- ity , that is, being about states of affairs, situations, or circumstances which make for their content. Arguably, it is precisely the aboutness of intentional states that can account for many of their hyperintensional features: as we think that 75 × 12 = 900, our thought is about these very integers, not about diophantine equations, elliptical curves, or else. Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 7 / 34
2. A Hyperintensional Semantics L with an indefinitely large set L AT of atoms p , q , r ( p 1 , p 2 , ... ), ¬ , ∧ , ∨ , ≺ , B , ( , ) . φ , ψ , χ , ..., are metavariables for formulas of L . Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 8 / 34
2. A Hyperintensional Semantics L with an indefinitely large set L AT of atoms p , q , r ( p 1 , p 2 , ... ), ¬ , ∧ , ∨ , ≺ , B , ( , ) . φ , ψ , χ , ..., are metavariables for formulas of L . The well-formed formulas are items in L AT and, if φ and ψ are formulas: ¬ φ | ( φ ∧ ψ ) | ( φ ∨ ψ ) | ( φ ≺ ψ ) | B φ ψ Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 8 / 34
2. A Hyperintensional Semantics L with an indefinitely large set L AT of atoms p , q , r ( p 1 , p 2 , ... ), ¬ , ∧ , ∨ , ≺ , B , ( , ) . φ , ψ , χ , ..., are metavariables for formulas of L . The well-formed formulas are items in L AT and, if φ and ψ are formulas: ¬ φ | ( φ ∧ ψ ) | ( φ ∨ ψ ) | ( φ ≺ ψ ) | B φ ψ ‘ B φ ψ ’ = ‘Conditional on φ , the agent believes ψ ’, or: ‘After revising by φ , the agent believes ψ ’ (‘static’ belief revision: [Board, 2004], [Asheim and Sövik, 2005], [Bonanno, 2005], [Leitgeb and Segerberg, 2005]). Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 8 / 34
2. A Hyperintensional Semantics A frame for L is a tuple F = � W , { R φ | φ ∈ L} , C , ⊕ , c � : W is a non-empty set of possible worlds; { R φ | φ ∈ L} is a set of accessibilities, R φ ⊆ W × W ; C is a set of contents : what the belief states are about ; ⊕ is fusion on C ; c : L AT → C . Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 9 / 34
2. A Hyperintensional Semantics A frame for L is a tuple F = � W , { R φ | φ ∈ L} , C , ⊕ , c � : W is a non-empty set of possible worlds; { R φ | φ ∈ L} is a set of accessibilities, R φ ⊆ W × W ; C is a set of contents : what the belief states are about ; ⊕ is fusion on C ; c : L AT → C . ⊕ satisfies, for all xyz ∈ C : (Idempotence) x ⊕ x = x (Commutativity) x ⊕ y = y ⊕ x (Associativity) ( x ⊕ y ) ⊕ z = x ⊕ ( y ⊕ z ) Franz Berto (F.Berto@uva.nl) Simple Hyperintensional Belief Revision Bochum, 15-16 Dec 2017 9 / 34
Recommend
More recommend
