Logic of Fiction and Logic of Fiction and Logic in Computer Logic in Computer

ScienceScience

Chayunt MathonChayunt Mathon

Department of Philosophy, Chulalongkorn Department of Philosophy, Chulalongkorn UniversityUniversityThailandThailand

FictionsFictions

Fictional DiscourseFictional Discourse

Fictive DiscourseFictive Discourse Metafictive DiscourseMetafictive Discourse Transitive DiscourseTransitive Discourse

Theories of FictionTheories of Fiction

Ontological Analysis Ontological Analysis Fictive-operator Analysis Fictive-operator Analysis Pretense, Imagination, and Pretense, Imagination, and

Make Believe AnalysisMake Believe Analysis

Fictional DiscourseFictional Discourse[Woods and Alward, 2004] though that the below aspects of fiction are axiom of [Woods and Alward, 2004] though that the below aspects of fiction are axiom of naïve theories of fictionality or naïve theories of fictionality or ourour pre-theoretic intuitions regarding pre-theoretic intuitions regarding fictions.Reference is possible to fictional beings even though they do not exit.fictions.Reference is possible to fictional beings even though they do not exit.

A. A. Some sentences about fictional beings and events are Some sentences about fictional beings and events are true.true.

B. B. Some inference about fictional beings and events are Some inference about fictional beings and events are correct.correct.

C. C. These three facts are name possible, in a central way, by These three facts are name possible, in a central way, by virtue of the creative authority of authors of fiction. virtue of the creative authority of authors of fiction. Indeed, the primary and originating criterion of truth for Indeed, the primary and originating criterion of truth for fictional sentences is the author’s sayso.fictional sentences is the author’s sayso.

D. D. These three facts are name possible, in a central way, by These three facts are name possible, in a central way, by virtue of the creative authority of authors of fiction. virtue of the creative authority of authors of fiction. Indeed, the primary and originating criterion of truth for Indeed, the primary and originating criterion of truth for fictional sentences is the author’s sayso.fictional sentences is the author’s sayso.

E. E. It is possible for a fictional truth to make reference to real It is possible for a fictional truth to make reference to real things. For example, “Sherlock Holmes lived in London” is things. For example, “Sherlock Holmes lived in London” is true and refers to the actual capital city of England.true and refers to the actual capital city of England.

Ontological ViewOntological View

This view believes that sentences of fictional and non-fictional discourse This view believes that sentences of fictional and non-fictional discourse have the same logical form, but a distinct range of entities serve as the have the same logical form, but a distinct range of entities serve as the semantic values of fictional and non-fictional expressions. The exemplars semantic values of fictional and non-fictional expressions. The exemplars are:are:

Qusasi-actualist MeinongeanQusasi-actualist Meinongean accounts accounts of the referents of fictional of the referents of fictional names ([Parsons, 1975] and [1980] and [Routley, 1979] and Cf. names ([Parsons, 1975] and [1980] and [Routley, 1979] and Cf. [Castaneda, 1979] and [Zalta, 1983]). The version of Parsons’ correlated [Castaneda, 1979] and [Zalta, 1983]). The version of Parsons’ correlated with each non-empty set of properties a distinct, specific object; existent with each non-empty set of properties a distinct, specific object; existent and non-existent. Fictional objects are a subclass of the class of non-and non-existent. Fictional objects are a subclass of the class of non-existent objects. They are the objects correlated with sets of the following existent objects. They are the objects correlated with sets of the following sort, where x is a fictional object:sort, where x is a fictional object:

x = the object correlated with {x = the object correlated with {pp: according to the relevant body of : according to the relevant body of literature, x has literature, x has pp}.}.

An example of this scheme is {An example of this scheme is {pp: according to the Conan Doyle stories, : according to the Conan Doyle stories, Sherlock Homes has Sherlock Homes has pp}. The consequence of such treat is that, fictional }. The consequence of such treat is that, fictional objects can enter to a sentence or the like and make it to have truth-value objects can enter to a sentence or the like and make it to have truth-value “true”.“true”.

Fictive-Operator AnalysisFictive-Operator AnalysisThis view believes that sentences of fictional and non-fictional discourse have different logical form. The sentences of This view believes that sentences of fictional and non-fictional discourse have different logical form. The sentences of fictional discourse are analyzed in term of tacit or explicit fictive operator. Each of the approach differs in fictional discourse are analyzed in term of tacit or explicit fictive operator. Each of the approach differs in interpretation of fictive operator. But their general scheme or logical form is interpretation of fictive operator. But their general scheme or logical form is

It is true-in-It is true-in-tt that that

Where Where tt is fictional text and is fictional text and is fictional sentence. For example, “It is true-in- is fictional sentence. For example, “It is true-in-the-Holmes-storiesthe-Holmes-stories that Sherlock Holmes that Sherlock Holmes was a detective.” The exemplars are:was a detective.” The exemplars are:

Possible world analysesPossible world analyses ([Plantinga, 1974] and [Kaplan, 1973] and [Gabriel, 1979] and[Lewis, 1983]). ([Plantinga, 1974] and [Kaplan, 1973] and [Gabriel, 1979] and[Lewis, 1983]). The version of Lewis’ truth theory of the fictional discourse is:The version of Lewis’ truth theory of the fictional discourse is:

A sentence of the form “It is true-in-A sentence of the form “It is true-in-tt that that ” is true iff ” is true iff is true at every world where t is told at known is true at every world where t is told at known fact fact rather than rather than fiction. fiction.

For example, “It is true-in-For example, “It is true-in-the-Holmes-storiesthe-Holmes-stories that Sherlock Holmes was a detective” is true just in case at all possible that Sherlock Holmes was a detective” is true just in case at all possible worlds in which the Holmes stories are told as known fact, the occupant of the Holmes-role is detective.worlds in which the Holmes stories are told as known fact, the occupant of the Holmes-role is detective.

Fictional world analysesFictional world analyses ([Howell, 1979] and [Pavel, 1986] and [Woltersdorff, 1980]). Simply, fictional ([Howell, 1979] and [Pavel, 1986] and [Woltersdorff, 1980]). Simply, fictional worlds are worlds of fiction, but they need not be consistent, even need not be complete. Such analyses interpret fictive worlds are worlds of fiction, but they need not be consistent, even need not be complete. Such analyses interpret fictive operator as:operator as:

““It is true-in-It is true-in-tt that that ” is (actually) true just in case ” is (actually) true just in case is true at all of the fictional worlds determined by is true at all of the fictional worlds determined by tt..

Non-referential, Non-referential, substitutional-quantificational substitutional-quantificational accountsaccounts [Woods, 1974]. The version of Woods’ truth [Woods, 1974]. The version of Woods’ truth theory of the fictional discourse is:theory of the fictional discourse is:

A sentence of the form “It is true-in-A sentence of the form “It is true-in-tt that that ” is true just in case either (1) ” is true just in case either (1) occurs in occurs in tt or (2) or (2) can be can be derived from sentences derived from sentences that occur in that occur in tt through repeated application of fictional-inference rule. through repeated application of fictional-inference rule.

Propositional attitude approachesPropositional attitude approaches [Curries, 1990]. Briefly, Curries would made the matefictive [Curries, 1990]. Briefly, Curries would made the matefictive claim “It is true-in-claim “It is true-in-tt that that ” to be analyzed as;” to be analyzed as;

The fictional author of The fictional author of tt believes that believes that ..

Where as “believe” is the attitude and fictional author is the subject of the attitude Cuuries chooses respectively.Where as “believe” is the attitude and fictional author is the subject of the attitude Cuuries chooses respectively.

Imaginative AnalysesImaginative AnalysesThis group of views is analyzed in term of some kind of imaginative activities. According to this kind of analyses, This group of views is analyzed in term of some kind of imaginative activities. According to this kind of analyses, storytellers do not assert the sentences they utter, nor do readers believe the sentences they encounter, they get storytellers do not assert the sentences they utter, nor do readers believe the sentences they encounter, they get “involved in the story” in certain way.“involved in the story” in certain way.

Authorial pretense analysesAuthorial pretense analyses [Searl, 1975]. The version of Searl’s truth theory of [Searl, 1975]. The version of Searl’s truth theory of the fictional discourse is:the fictional discourse is:

Authors do not assert sentences they utter, they Authors do not assert sentences they utter, they pretendpretend to do so; and part to do so; and part of this pretense of this pretense involves pretending to refer to real individuals (in the case of involves pretending to refer to real individuals (in the case of

the sentences contain the sentences contain fictional names). In this manner, authors fictional names). In this manner, authors createcreate fictional characters and events. When fictional characters and events. When critics or readers say that critics or readers say that they really refer they really refer

to the fictional entity in to the fictional entity in , they do so , they do so because because of the of the shared pretenseshared pretense..

Reader/appreciator make-believe analysesReader/appreciator make-believe analyses [Walton, 1990]. According to the [Walton, 1990]. According to the version of Walton, games of make-believe are rule-governed activities. Such rules version of Walton, games of make-believe are rule-governed activities. Such rules prescribe that particular propositions be imagined. These are the fictional truths of prescribe that particular propositions be imagined. These are the fictional truths of the game. A prop in a game of make-believe is an object that, in virtue of the rules of the game. A prop in a game of make-believe is an object that, in virtue of the rules of the game, generates fictional truths. Here is his theory:the game, generates fictional truths. Here is his theory:

A sentence of the form “It is true-in-A sentence of the form “It is true-in-tt that S” is true iff fiction that S” is true iff fiction tt is such that is such that one who engages one who engages in pretense of kind K in a game authorized for it makes it in pretense of kind K in a game authorized for it makes it fictional of herself that she fictional of herself that she speaks trulyspeaks truly

For example: “it is true-in-For example: “it is true-in-The Hound of the BaskervillesThe Hound of the Baskervilles that Holmes was a that Holmes was a detective” has to be paraphrased as “detective” has to be paraphrased as “The Hound of the Baskervilles The Hound of the Baskervilles is such that one is such that one who engages in pretense of kind K in a game authorized for it to makes it fictional of who engages in pretense of kind K in a game authorized for it to makes it fictional of herself that she speaks truly.”herself that she speaks truly.”

Nature of FictionsNature of Fictions

““A fiction is a made-up story.”A fiction is a made-up story.” (Scholes, Robert (1991) (Scholes, Robert (1991) Element of LiteratureElement of Literature))

““There’s no one “right” way to read a piece of fiction. There’s no one “right” way to read a piece of fiction. There are many good ways. This does There are many good ways. This does notnot mean that mean that anyone’s reading of a piece of fiction is equal to anyone anyone’s reading of a piece of fiction is equal to anyone else’s. else’s. There are better and worse readingThere are better and worse reading, depending on , depending on how well readers can attune themselves to the story, on how well readers can attune themselves to the story, on how carefully they have looked at the language, become how carefully they have looked at the language, become aware of the tone, understood the theme, notice patterns aware of the tone, understood the theme, notice patterns of imagery, and, in general, become quite and really of imagery, and, in general, become quite and really listened to a separate human being. But given equal listened to a separate human being. But given equal attention and sensitivity to a story, there are many attention and sensitivity to a story, there are many legitimate legitimate approachesapproaches.”.” (Clayton, John J. (2000) (Clayton, John J. (2000) The Heath Introduction to The Heath Introduction to FictionFiction ) )

Structure of Formal logical Structure of Formal logical SystemSystem

GrammarGrammar: : formal Language/symbols formal Language/symbols Deductive ApparatusDeductive Apparatus: axiom(s)/ : axiom(s)/

Rules of InferenceRules of Inference

Proof TheoryProof Theory

SemanticsSemantics: : Interpretations of formal Interpretations of formal languagelanguage

Historical sematics Historical sematics approach of Logic of Fictionapproach of Logic of Fiction We, intuitively, can valuate a metafictive We, intuitively, can valuate a metafictive

propositionproposition to be TRUEto be TRUE Denying the Objectual Interpretation of Denying the Objectual Interpretation of

Classical LogicClassical Logic (only FALSE value can be (only FALSE value can be given for a metafictive proposition)given for a metafictive proposition)

The relevant semantics is ordinary Model-The relevant semantics is ordinary Model-TheoreticTheoretic

A metafictive proposition can be TRUE A metafictive proposition can be TRUE because of an aspect of Correspondence because of an aspect of Correspondence Theory of Truth; the story say soTheory of Truth; the story say so or the author or the author say so.say so.

Historical systematic Historical systematic approach toapproach to the Logic of the Logic of

FictionFiction Woods, John (1974), Woods, John (1974), The Logic of Fiction: Philosophical The Logic of Fiction: Philosophical

Sounding of Deviant LogicSounding of Deviant Logic......

Nossum, Rolf (2003), ‘A Contextual Approach to the Logic Nossum, Rolf (2003), ‘A Contextual Approach to the Logic of Fiction’, LNAI 2680of Fiction’, LNAI 2680

..

..

..

Woods, John and Peter Alward (2004). “The Logic of Woods, John and Peter Alward (2004). “The Logic of Fiction” In Gabbay, D. M. (ed.), Fiction” In Gabbay, D. M. (ed.), Handbook of Philosophical Handbook of Philosophical LogicLogic

Logic of Fiction vs. logics in Logic of Fiction vs. logics in computer sciencecomputer science

Logic in computer scienceLogic in computer science:topics where logic is applied to computer science and artificial :topics where logic is applied to computer science and artificial

intelligenceintelligence: logic has important role in some area of computer science in general : logic has important role in some area of computer science in general

and AI in particularand AI in particular

Unconcerned logics: Unconcerned logics: Boolean Logic, Fuzzy Boolean Logic, Fuzzy Logic, Quantum Logic, etc.Logic, Quantum Logic, etc.

Concerned logics: Concerned logics: - - Common Sense Logicism Common Sense Logicism [including [including narrative narrative understanding]understanding] (AI); John (AI); John McCarthyMcCarthy- - The Default based logics/kinds of The Default based logics/kinds of Nonmonotonic Logics; Belief Revision Nonmonotonic Logics; Belief Revision (AI); (AI); Closed –world reasoning Closed –world reasoning (Database of (Database of computer computer science); science); Rational PlanningRational Planning

Woods, John and Peter Woods, John and Peter Alward (2004). “The Logic Alward (2004). “The Logic

of Fiction”of Fiction” Take the ordinary Model-TheoreticTake the ordinary Model-Theoretic

Semantics.Semantics.

YetYet In Proof Theory; proposedIn Proof Theory; proposed

1. 1. defaultdefault [(Reiter, 1980); (Makinson, [(Reiter, 1980); (Makinson, 1993) …) as Generic proposition 1993) …) as Generic proposition (The default (The default that Holmes has a skin is derived from the generic proposition that that Holmes has a skin is derived from the generic proposition that humans have skins + Holmes is a human.)humans have skins + Holmes is a human.)

2. 2. Implicatures [(Grice, 1989); Implicatures [(Grice, 1989); (Levinson, 2000)] as speaker’s (Levinson, 2000)] as speaker’s common common knowledgeknowledge

Monotonic-Nonmonotonic Monotonic-Nonmonotonic LogicsLogics

MonotonicMonotonic LogicLogic

- - Aristotelian logic Aristotelian logic

-- Classical logic Classical logic

- deal only with - deal only with patterns of patterns of inference that hold inference that hold without exceptionwithout exception

Nonmonotonic Nonmonotonic LogicsLogics

- - It is reasonable to It is reasonable to ignore outlandish ignore outlandish possibilities.possibilities.

Default based logicDefault based logic

To ignore outlandish possibilitiesTo ignore outlandish possibilities is to is to have have default(s)default(s)..

Manipulate some Default Rule; for Manipulate some Default Rule; for exampleexample

- General form: General form:

In the presence of {In the presence of {AA11,…,,…,AAnn}} and in the absence ofand in the absence of {{BB11,…,,…,BBnn}, conclude }, conclude CC..

- Normal default form: General form: Normal default form: General form:

In the presence of {In the presence of {AA11,…,,…,AAnn}} and in the absence ofand in the absence of --CC, conclude , conclude CC..

RecallRecall

(Clayton, John J. (2000) (Clayton, John J. (2000) The Heath The Heath Introduction to FictionIntroduction to Fiction ) )

““There’s no one “right” way to read a piece of There’s no one “right” way to read a piece of fiction. There are many good ways. This does fiction. There are many good ways. This does notnot mean that anyone’s reading of a piece of fiction is mean that anyone’s reading of a piece of fiction is equal to anyone else’s. equal to anyone else’s. There are better and worse There are better and worse readingreading, depending on how well readers can attune , depending on how well readers can attune themselves to the story, on how carefully they have themselves to the story, on how carefully they have looked at the language, become aware of the tone, looked at the language, become aware of the tone, understood the theme, notice patterns of imagery, understood the theme, notice patterns of imagery, and, in general, become quite and really listened to and, in general, become quite and really listened to a separate human being. But given equal attention a separate human being. But given equal attention and sensitivity to a story, there are many legitimate and sensitivity to a story, there are many legitimate approachesapproaches.”.”

ANDAND

Need of ordinary Model-TheoreticNeed of ordinary Model-Theoretic

What should we concern in What should we concern in logics in Computer logics in Computer

Science?Science?

No: values; 0, 1No: values; 0, 1 No: Physical status of 0/1 values, No: Physical status of 0/1 values,

0v., 5v 0v., 5v

Yes: the informal reading of the Yes: the informal reading of the values 0, 1 (the informal semantics)values 0, 1 (the informal semantics)

Informal semantics Informal semantics approachapproach

Logic of Fiction (Philosophical) Logic of Fiction (Philosophical)

= = many values logic, bivalence logic with truth many values logic, bivalence logic with truth valueless proposition (?), mixed semantics valueless proposition (?), mixed semantics

(at (at least least one of them must be ordinary one of them must be ordinary Model-Theoretic)Model-Theoretic)

≠≠ ordinary Model-Theoretic ordinary Model-Theoretic withwith default based default based proof theoryproof theory

logic of fictions (Computer Science/AI, default logic of fictions (Computer Science/AI, default based ) based )

= = Non-ordinary Model-Theoretic semantics; for Non-ordinary Model-Theoretic semantics; for example, Preference Model-Theoretic, othersexample, Preference Model-Theoretic, others

≠ ≠ sole ordinary Model-Theoretic sole ordinary Model-Theoretic (because of the nature (because of the nature of of fictions human should care)fictions human should care)