How to play games with types Ellen Breitholtz and Robin Cooper - PowerPoint PPT Presentation

How to play games with types Ellen Breitholtz and Robin Cooper Centre for Linguistic Theory and Studies in Probability (CLASP) Department of Philosophy, Linguistics and Theory of Science (FLoV) Supported in part by VR project 2016-01162, Incremental Reasoning in Dialogue (IncReD) and Riksbankens Jubileumsfond project P16-0805:1, Dialogical Reasoning in Patients with Schizophrenia (DRiPS) .

Outline TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi

Outline TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Language as action ◮ Language as action (Austin, 1962; Lewis, 1969; Clark, 1996; Barwise and Perry, 1983) ◮ Agents need to coordinate action: coordination games (Lewis, 1969) 4 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Two kinds of games ◮ Dialogue games build on techniques used in coordination games involving non-linguistic agents ◮ Interaction games in TTR, a type theory with records (Cooper, 2014; Breitholtz, 2014; Cooper, in prep) ◮ Social meaning games Burnett (fthc), drawing on techniques from Game Theory (GT) Lewis (1969) ◮ Combining these types of games in terms of a theory of dialogue involving Information State Update : Ginzburg’s KoS (Ginzburg, 2012) 5 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Potential contributions – KoS-TTR ◮ a framework for choosing which games to play ◮ an account of misunderstandings about which game is being played ◮ accommodation of games on the basis of interlocutor’s behaviour ◮ explain how a single action can represent a move in more than one game — What’s cookin’? 6 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Potential contributions – GT ◮ an account of variation in probabilistic terms ◮ a variety of overall interactive strategies: ◮ male rationalism – maximize own utility ◮ collaborative – maximize utility (regardless of whose) ◮ altruistic – maximize other’s utility ◮ a theory of strategy in non-deterministic games ◮ a way of accounting for choice in dialogues where the opinion or world view of the receiver is important, such as argumentative dialogue 7 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Potential contributions – GT ◮ an account of variation in probabilistic terms ◮ a variety of overall interactive strategies: ◮ male rationalism – maximize own utility ◮ collaborative – maximize utility (regardless of whose) ◮ altruistic – maximize other’s utility ◮ a theory of strategy in non-deterministic games ◮ a way of accounting for choice in dialogues where the opinion or world view of the receiver is important, such as argumentative dialogue 7 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Games in TTR ◮ Cooper (in prep), Ch. 1 (discussed here) ◮ Breitholtz (2014) in relation to enthymematic reasoning ◮ related to Ginzburg on genre and conversation types 8 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Fetch – a game of interaction and coordination 9 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Query – is this the beginning of an event of type FetchGame ? 10 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Creation – the dog must predict and carry out its contribution to an event of type FetchGame 11 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi String types cf. work by Tim Fernando, e.g. Fernando (2015) 1. if T 1 , T 2 ∈ Type , then T 1 ⌢ T 2 ∈ Type a : T 1 ⌢ T 2 iff a = x ⌢ y , x : T 1 and y : T 2 2. if T ∈ Type then T + ∈ Type . a : T + iff a = x ⌢ 1 . . . ⌢ x n , n > 0 and for i , 1 ≤ i ≤ n , x i : T . . . 12 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi A game of fetch 1 ¡ 2 ¡ 0 ¡ 3 ¡ 6 ¡ 4 ¡ 5 ¡ 13 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi A game of fetch 1 ¡ 2 ¡ 0 ¡ 3 ¡ 6 ¡ 4 ¡ 5 ¡ (pick up( a , c ) ⌢ attract attention( a , b ) ⌢ throw( a , c ) ⌢ run after( b , c ) ⌢ pick up( b , c ) ⌢ return( b , c , a )) + 13 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Information states and gameboards ◮ Information states (gameboards) are used by agents to keep track of where they are in the creation of an event belonging to a certain type ◮ each agent has their own view of the state of the game ◮ plays an essential role in coordination ◮ information state (Larsson, 2002) and gameboard (Ginzburg, 1994, 2012, originally Lewis, 1979) are adopted from the literature on dialogue ◮ we shall model information states as records and use ‘gameboard’ to refer to types of information states 14 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi The types InfoState and InitInfoState � � InfoState agenda : [ RecType ] � � InitInfoState agenda=[] : [ RecType ] 15 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Game of fetch (human, a , dog, b , and stick, c ) ◮ game as a set of update functions corresponding to transitions in a finite state automaton ◮ an initial update function � � λ r : agenda=[]:[ RecType ] . � � � � agenda=[ e:pick up( a , c ) ]:[ RecType ] ◮ a non-initial, non-final update function � � � � λ r : agenda=[ e:pick up( a , c ) ]:[ RecType ] � � λ e : e:pick up( a , c ) . � � � � agenda=[ e:attract attention( a , b ) ]:[ RecType ] ◮ a final update function � � � � λ r : agenda=[ e:return( b , c , a ) ]:[ RecType ] � � λ e : e:return( b , c , a ) . � � agenda=[]:[ RecType ] 16 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Corresponding action rules � � r : A agenda=[]:[ RecType ] r is A ’s current info state � � � � : A agenda=[ e:pick up( a , c ) ]:[ RecType ] ! If A judges the current information state to have an empty agenda then A is licensed to create an information state where an event type of a picking up c is on the agenda. � � � � � � r : A agenda=[ e:pick up( a , c ) ]:[ RecType ] e : A e:pick up( a , c ) � � � � : A agenda=[ e:attract attention( a , b ) ]:[ RecType ] ! 17 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Game of fetch (with roles abstracted)  h : Ind  c human : human(h)     d : Ind λ r ∗ :   .   c dog : dog(d)     s : Ind   c stick : stick(s) � � { λ r : agenda=[]:[ RecType ] . e:pick up( r ∗ .h, r ∗ .s) � � � � agenda=[ ]:[ RecType ] , e:pick up( r ∗ .h, r ∗ .s) � � � � λ r : agenda=[ ]:[ RecType ] e:pick up( r ∗ .h, r ∗ .s) � � λ e : . � � e:attract attention( r ∗ .h, r ∗ .d) � � agenda=[ ]:[ RecType ] , . . . , � e:return( r ∗ .d, r ∗ .s, r ∗ .h) � λ e : . � � agenda=[]:[ RecType ] } 18 / 47

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi A problem ◮ There is no mechanism for deciding which strategy to choose in non-deterministic games. (More than one update function that can be applied.) ◮ Solution: Use GT game similar to Burnett’s social meaning games associated with variation. 19 / 47

Outline TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi

TTR Games in a theory of language as action Social meaning games in GT Relating the two notions of game Argument games using topoi Obama ◮ Use of -ing/-in’ verbal morphology (Labov, 2012, p. 22, cited by Burnett and Smith) ◮ at a barbeque — 72% -in’ ◮ meeting press after barbecue — 33% -in’ ◮ acceptance speech at Democratic National Convention — 3% -in’ 21 / 47