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1/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
A logic for reasoning about counterfactualemotions
Emiliano Lorini and Francois SchwarzentruberIRIT, Toulouse, France
1/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
2/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Outline
1 IntroductionTopic of this talkState of the artIngredients
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
2/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
3/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Example: “rock-paper-scissors” game
“rock-paper-scissors” game rule
� � � etc.
3/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
4/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Example: “rock-paper-scissors” game
“rock-paper-scissors” game rule
� � � etc.
Here Roberta regrets having played "paper".4/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
5/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Example: “rock-paper-scissors” game
“rock-paper-scissors” game rule
� � � etc.
Indeed... she could have won by playing rock.5/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
6/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Example: “rock-paper-scissors” game
Aim: to provide a logical framework for reasoning aboutcounterfactual emotions.
Applications: video games, robots assisting humans, etc.
6/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
7/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Outline
1 IntroductionTopic of this talkState of the artIngredients
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
7/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
8/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
State of the art
No comprehensive formal model of counterfactual emotionslike:
regret, rejoicing;
guilt, shame.
8/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
9/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Outline
1 IntroductionTopic of this talkState of the artIngredients
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
9/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
10/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Ingredients we need
Counterfactual emotions like regret are based on an agent’salteration of a factual situation and in the imagination of analternative situation that could have realized if somethingdifferent was done (Kahnemann & Miller, 1986)
We need:
Logic of agency for expressing counterfactual facts;
Imagination;
Time;
Preferences.
10/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
11/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Ingredients we will use
Counterfactual emotions like regret are based on an agent’salteration of a factual situation and in the imagination of analternative situation that could have realized if somethingdifferent was done (Kahnemann & Miller, 1986)
We will use:
Logic of agency for expressing counterfactual facts:Chellas’ STIT modal logic;
Imagination: modal epistemic logic;
Time (this work is preliminary... but it is a perspective);
Preferences: simple constructions with propositions.
11/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
12/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Topic of this talkState of the artIngredients
Table of Contents
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
12/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
13/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statementsWhy STIT?SyntaxSemanticsExpressing counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives13/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
14/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
CL, ATL VS STIT
In CL, ATL, we can express what agents can do;
In STIT, we also express what agents do.
→ STIT more suitable for counterfactual statements.
14/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
15/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statementsWhy STIT?SyntaxSemanticsExpressing counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives15/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
16/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Syntax
DefinitionLanguage LgroupSTIT:
ϕ ::= p | ϕ ∧ ϕ | ¬ϕ | [J]ϕ
where J ⊆ AGT .
As usual, 〈J〉ϕ def= ¬[J]¬ϕ.
[J]ϕ means “group J sees to it that ϕ” ≡ “group J choosesactions such that whatever group J does, ϕ is true”.
16/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
17/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example
[J]ϕ means “whatever group J does, ϕ is true”.
[Roberta]paperRoberta
“Roberta chooses an action such that whatever Bob does,paperRoberta is true”
17/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
18/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example: [∅] for expressing “necessarly”
[∅]ϕ means “whatever group AGT does, ϕ is true” ≡“necessarly, ϕ is true”.
[∅](paperRoberta ∨ scissorsRoberta ∨ rockRoberta)“necessarly we have (paperRoberta ∨ scissorsRoberta ∨ rockRoberta)”
18/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
19/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example: expressing ability with 〈∅〉[J]
〈∅〉[Roberta]rockRoberta
“it is possible that Roberta chooses an action such that whatever Bobdoes, rockRoberta is true”
19/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
20/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example: the dual operator 〈J〉
[J]ϕ means “whatever group J does, ϕ is true”〈J〉ϕ means “there exists actions for group J such that ϕ” ≡“group J allows that ϕ is true”.
〈Bob〉winRoberta
“the choose of Bob allows Roberta to win”
20/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
21/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statementsWhy STIT?SyntaxSemanticsExpressing counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives21/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
22/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example of a groupSTIT-model
A groupSTIT-model is a strategic form game model.
22/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
23/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
groupSTIT-model
Definition
A groupSTIT-model is M = 〈W , R, V 〉 such that:
W 6= ∅;R : 2AGT → 2W×W such that:
for all G ⊆ AGT , RG is an equivalence relation over W ;for all G ⊆ AGT , RG ⊆ R∅;for all G ⊆ AGT , RG =
⋂a∈G R{a};
for all (xa)a∈AGT ∈ W AGT ,⋂
a∈AGT R{a}(xa) 6= ∅.
V : W → 2ATM .
A groupSTIT-model is a strategic form game model.
23/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
24/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Truth definitions
Definition
M, w |= [J]ϕ iff for all v ∈ RJ(w),M, v |= ϕ.
M, w |= [Roberta]paperRoberta.24/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
25/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Illustrating truth definitions
M, w |= [∅](paperRoberta ∨ scissorsRoberta ∨ rockRoberta).
25/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
26/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Illustrating truth definitions
M, w |= 〈∅〉[Roberta]rockRoberta.
26/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
27/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Illustrating truth definitions
〈Bob〉winRoberta means “there exists an action for Roberta suchthat winRoberta.”.
M, w |= 〈Bob〉winRoberta.27/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
28/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statementsWhy STIT?SyntaxSemanticsExpressing counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives28/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
29/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example: “rock-paper-scissors” game
Here Roberta looses.
29/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
30/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Example: “rock-paper-scissors” game
But Roberta “could have prevented it” by playing "rock" instead.
30/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
31/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
We can see it on the STIT-model
M, w |= ¬winRoberta ∧ 〈Bob〉winRoberta.
31/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
32/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
We can see it on the STIT-model
M, w |= ¬winRoberta ∧ 〈Roberta〉winRoberta.
32/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
33/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Why STIT?SyntaxSemanticsExpressing counterfactual statements
Counterfactual statements in STIT
Definition
CHPJχdef= χ ∧ 〈J〉¬χ
CHPJ means “group J could have prevented χ to be true”:
χ is true;
Other agents allows ¬χ.
33/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
34/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicingAdding knowledgeAdding preferencesExpressing regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
34/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
35/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Extending STIT with knowledge
DefinitionLanguage LKSTIT :
ϕ ::= p | ϕ ∧ ϕ | ¬ϕ | [J]ϕ | Kiϕ
where J ⊆ AGT and i ∈ AGT .
Kiϕ means “agent i knows ϕ.”
35/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
36/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Semantics of KSTIT
Definition
A KSTIT-model is M = (W , {RJ}J⊆AGT , {Ei}i∈AGT , V ) where:
(W , {RJ}J⊆AGT , V ) is a STIT-model;
For all i ∈ AGT , Ei is an equivalence relation.
Definition
M, w |= Kiϕ iff for all v ∈ Ei(w),M, v |= ϕ.
36/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
37/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicingAdding knowledgeAdding preferencesExpressing regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
37/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
38/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Adding preferences
The special atom goodi identifies good states for agent i .
GOODiχdef= [∅](goodi → χ)
GOODiχ ≈ “χ is good for agent i”
DESiχdef= KiGOODiχ
DESiχ ≈ “χ is desirable for agent i”
38/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
39/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Some properties of agents’ preferences
Deductive closure:|=KSTIT (DESiχ1 ∧ DESi(χ1 → χ2)) → DESiχ2;
Positive introspection: |=KSTIT DESiχ ↔ KiDESiχ;
Negative introspection: |=KSTIT ¬DESiχ ↔ Ki¬DESiχ
39/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
40/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicingAdding knowledgeAdding preferencesExpressing regret and rejoicing
4 Decidability of the satisfiability problem
5 Perspectives
40/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
41/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Regret
Definition
REGRETiχdef= DESi¬χ ∧ KiCHPiχ
where CHPiχdef= χ ∧ 〈AGT \ {i}〉¬χ.
Agent i regrets that χ is true (REGRETiχ):
¬χ is desirable for i ;
i knows that it could have prevented χ to be true now.
41/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
42/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Regret: a little remark about action and effect
Explicit action I regret having played "paper".l l
Implicit action (effect) I regret my action such that ¬winRoberta.
42/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
43/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Rejoicing
REGRETiχdef= DESi¬χ ∧ KiCHPiχ
↓
rejoicing is the positive counterpart of regret (see, e.g.,Zeelenberg et al., 1996)
↓
Definition (Agent i rejoices over χ)
REJOICEiχdef= DESiχ ∧ KiCHPiχ
43/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
44/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Adding knowledgeAdding preferencesExpressing regret and rejoicing
Properties of regret and rejoicing
Positive and negative introspections of regret and rejoicing:|=KSTIT REGRETiχ ↔ KiREGRETiχ;|=KSTIT REJOICEiχ ↔ KiREJOICEiχ;|=KSTIT ¬REGRETiχ ↔ Ki¬REGRETiχ;|=KSTIT ¬REJOICEiχ ↔ Ki¬REJOICEiχ.
Regret implies desire frustration:|=KSTIT REGRETiχ → (DESi¬χ ∧ Kiχ);
Rejoice implies desire satisfaction:|=KSTIT REJOICEiχ → (DESiχ ∧ Kiχ).
44/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
45/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problemMotivationWhole STITSolution: a fragment of STIT
5 Perspectives
45/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
46/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Motivation for studying decidability
Is it possible for robots to reason about regret, rejoicing?
How difficult will it be for them?
46/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
47/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problemMotivationWhole STITSolution: a fragment of STIT
5 Perspectives
47/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
48/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Whole STIT is expressive
KSTIT is very expressive.
Example (Compassion)
I regret that you regret p.
and...
48/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
49/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Complexity of the whole STIT
Theorem
(Herzig & Schwarzentruber, 2008) The STIT-satisfiabilityproblem is:
NP-complete if card(AGT ) = 1;
NEXPTIME-complete if card(AGT ) = 2;
undecidable if card(AGT ) ≥ 3.
49/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
50/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Outline
1 Introduction
2 Chellas’ STIT for counterfactual statements
3 Counterfactual emotions: Regret and rejoicing
4 Decidability of the satisfiability problemMotivationWhole STITSolution: a fragment of STIT
5 Perspectives
50/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
51/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Solution: reducing expressivity
We deny:
I regret that you regret p.
We accept:
I regret (p ∨ q).
51/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
52/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Solution: a fragment dfSTIT
whole STIT
〈Sam〉([Bob]p ∧ [Sam]([Robert ]q ∨ 〈Bob, Robert〉p))
The fragment dfSTIT
[Bob](p ∨ q) ∧ 〈∅〉[Robert , Bob](p ∧ r)
52/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
53/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Definition of the fragment dfSTIT
DefinitionThe language LdfSTIT:
χ ::= ⊥ | p | χ ∧ χ | ¬χ (propositional formulas)
ψ ::= [J]χ | ψ ∧ ψ (STIT formulas conjunction)
ϕ ::= χ | ψ | ϕ ∧ ϕ | ¬ϕ | 〈∅〉ψ (STIT and “can” formulas)
where J ∈ 2AGT \ {∅}.
53/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
54/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
dfSTIT is decidable
Theorem
The dfSTIT-satisfiability problem is NP-complete whatevercard(AGT ).
LdfSTIT
LgroupSTIT
54/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
55/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
Extending STIT with knowledge
Definition
Language of dfKSTIT:
χ ::= ⊥ | p | χ ∧ χ | ¬χ (propositional formulas)
ψ ::= [J]χ | ψ ∧ ψ (STIT formulas conjunction)
ϕ ::= χ | ψ | ϕ ∧ ϕ | ¬ϕ | 〈∅〉ψ | Kiϕ (see-to-it, “can”,knowledge formulas )
where i ∈ AGT and J ∈ 2AGT \ {∅}.
55/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
56/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
MotivationWhole STITSolution: a fragment of STIT
dfKSTIT is decidable
Theorem
The satisfiability problem of dfKSTIT is:
NP-complete if card(AGT ) = 1;
PSPACE-complete if card(AGT ) ≥ 2.
56/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
57/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Perspectives
axiomatisation for the fragment?
add time?
improve modelisation of preferences?
find a more expressive fragment?
norms: guilt, shame?
57/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
58/58
IntroductionChellas’ STIT for counterfactual statements
Counterfactual emotions: Regret and rejoicingDecidability of the satisfiability problem
Perspectives
Thank you!
58/58 Emiliano Lorini and Francois Schwarzentruber IRIT, Toulouse, FranceA logic for reasoning about counterfactual emotions
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