Logic of Fiction and Logic in Computer Science

1. Logic of Fiction and Logic in Computer Science Chayunt Mathon Department of Philosophy, Chulalongkorn University Thailand

2. Fictional Discourse Fictive Discourse Metafictive Discourse Transitive Discourse Theories of Fiction Ontological Analysis Fictive-operator Analysis Pretense, Imagination, and Make Believe Analysis Fictions

3. Fictional Discourse [Woods and Alward, 2004] though that the below aspects of fiction are axiom of naïve theories of fictionality or our pre-theoretic intuitions regarding fictions.Reference is possible to fictional beings even though they do not exit. A. Some sentences about fictional beings and events are true. B. Some inference about fictional beings and events are correct. C. These three facts are name possible, in a central way, by virtue of the creative authority of authors of fiction. Indeed, the primary and originating criterion of truth for fictional sentences is the author’s sayso. D. These three facts are name possible, in a central way, by virtue of the creative authority of authors of fiction. Indeed, the primary and originating criterion of truth for fictional sentences is the author’s sayso. E. It is possible for a fictional truth to make reference to real things. For example, “Sherlock Holmes lived in London” is true and refers to the actual capital city of England.

4. Ontological View 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 semantic values of fictional and non-fictional expressions. The exemplars are: • Qusasi-actualist Meinongean accounts of the referents of fictional names ([Parsons, 1975] and [1980] and [Routley, 1979] and Cf. [Castaneda, 1979] and [Zalta, 1983]). The version of Parsons’ correlated 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-existent objects. They are the objects correlated with sets of the following sort, where x is a fictional object: x = the object correlated with {p: according to the relevant body of literature, x has p}. An example of this scheme is {p: according to the Conan Doyle stories, Sherlock Homes has p}. The consequence of such treat is that, fictional objects can enter to a sentence or the like and make it to have truth-value “true”.

5. Fictive-Operator Analysis 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 interpretation of fictive operator. But their general scheme or logical form is It is true-in-t that  Where t is fictional text and  is fictional sentence. For example, “It is true-in-the-Holmes-stories that Sherlock Holmes was a detective.” The exemplars are:  Possible world analyses ([Plantinga, 1974] and [Kaplan, 1973] and [Gabriel, 1979] and[Lewis, 1983]). The version of Lewis’ truth theory of the fictional discourse is: A sentence of the form “It is true-in-t that ” is true iff  is true at every world where t is told at known fact rather than fiction. For example, “It is true-in-the-Holmes-stories 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.  Fictional world analyses ([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 operator as: “It is true-in-t that ” is (actually) true just in case  is true at all of the fictional worlds determined by t.  Non-referential, substitutional-quantificational accounts [Woods, 1974]. The version of Woods’ truth theory of the fictional discourse is: A sentence of the form “It is true-in-t that ” is true just in case either (1)  occurs in t or (2)  can be derived from sentences that occur in t through repeated application of fictional-inference rule.  Propositional attitude approaches [Curries, 1990]. Briefly, Curries would made the matefictive claim “It is true-in-t that ” to be analyzed as; The fictional author of t believes that . Where as “believe” is the attitude and fictional author is the subject of the attitude Cuuries chooses respectively.

6. Imaginative 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 “involved in the story” in certain way.  Authorial pretense analyses [Searl, 1975]. The version of Searl’s truth theory of the fictional discourse is: Authors do not assert sentences they utter, they pretend to do so; and part of this pretense involves pretending to refer to real individuals (in the case of the sentences contain fictional names). In this manner, authors create fictional characters and events. When critics or readers say that  they really refer to the fictional entity in , they do so because of the shared pretense.  Reader/appreciator make-believe analyses [Walton, 1990]. According to the 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 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: A sentence of the form “It is true-in-t that S” is true iff fiction t is such that one who engages in pretense of kind K in a game authorized for it makes it fictional of herself that she speaks truly For example: “it is true-in-The Hound of the Baskervilles that Holmes was a detective” has to be paraphrased as “The Hound of the Baskervilles is such that one who engages in pretense of kind K in a game authorized for it to makes it fictional of herself that she speaks truly.”

7. Nature of Fictions • “A fiction is a made-up story.”(Scholes, Robert (1991) Element of Literature) • “There’s no one “right” way to read a piece of fiction. There are many good ways. This does not mean that anyone’s reading of a piece of fiction is equal to anyone else’s. There are better and worse reading, depending on how well readers can attune themselves to the story, on how carefully they have looked at the language, become aware of the tone, understood the theme, notice patterns of imagery, and, in general, become quite and really listened to a separate human being. But given equal attention and sensitivity to a story, there are many legitimate approaches.”(Clayton, John J. (2000) The Heath Introduction to Fiction )

8. Structure of Formal logical System • Grammar: formal Language/symbols • Deductive Apparatus: axiom(s)/ Rules of Inference  Proof Theory • Semantics: Interpretations of formal language

9. Historical sematics approach of Logic of Fiction • We, intuitively, can valuate a metafictive propositionto be TRUE • Denying the Objectual Interpretation of Classical Logic(only FALSE value can be given for a metafictive proposition) • The relevant semantics is ordinary Model-Theoretic • A metafictive proposition can be TRUE because of an aspect of Correspondence Theory of Truth; the story say soor the author say so.

10. Historical systematic approach tothe Logic of Fiction • Woods, John (1974), The Logic of Fiction: Philosophical Sounding of Deviant Logic . . . • Nossum, Rolf (2003), ‘A Contextual Approach to the Logic of Fiction’, LNAI 2680 . . . • Woods, John and Peter Alward (2004). “The Logic of Fiction” In Gabbay, D. M. (ed.), Handbook of Philosophical Logic

11. Logic of Fiction vs. logics in computer science

12. Logic in computer science:topics where logic is applied to computer science and artificial intelligence: logic has important role in some area of computer science in general and AI in particular • Unconcerned logics: Boolean Logic, Fuzzy Logic, Quantum Logic, etc. • Concerned logics: - Common Sense Logicism [including narrative understanding] (AI); John McCarthy - The Default based logics/kinds of Nonmonotonic Logics; Belief Revision (AI); Closed –world reasoning (Database of computer science); Rational Planning

13. Woods, John and Peter Alward (2004). “The Logic of Fiction” • Take the ordinary Model-TheoreticSemantics. Yet • In Proof Theory; proposed 1. default [(Reiter, 1980); (Makinson, 1993) …) as Generic proposition (The default that Holmes has a skin is derived from the generic proposition that humans have skins + Holmes is a human.) 2. Implicatures [(Grice, 1989); (Levinson, 2000)] as speaker’s common knowledge

14. MonotonicLogic - Aristotelian logic - Classical logic - deal only with patterns of inference that hold without exception Nonmonotonic Logics - It is reasonable to ignore outlandish possibilities. Monotonic-Nonmonotonic Logics

15. Default based logic • To ignore outlandish possibilitiesis to have default(s). • Manipulate some Default Rule; for example • General form: In the presence of {A1,…,An}and in the absence of{B1,…,Bn}, conclude C. • Normal default form: General form: In the presence of {A1,…,An}and in the absence of-C, conclude C.

16. Recall (Clayton, John J. (2000) The Heath Introduction to Fiction ) “There’s no one “right” way to read a piece of fiction. There are many good ways. This does not mean that anyone’s reading of a piece of fiction is equal to anyone else’s. There are better and worse reading, depending on how well readers can attune themselves to the story, on how carefully they have looked at the language, become aware of the tone, understood the theme, notice patterns of imagery, and, in general, become quite and really listened to a separate human being. But given equal attention and sensitivity to a story, there are many legitimate approaches.”

17. AND Need of ordinary Model-Theoretic

18. What should we concern in logics in Computer Science? • No: values; 0, 1 • No: Physical status of 0/1 values, 0v., 5v • Yes: the informal reading of the values 0, 1 (the informal semantics)

19. Informal semantics approach • Logic of Fiction (Philosophical) = many values logic, bivalence logic with truth valueless proposition (?), mixed semantics (at least one of them must be ordinary Model-Theoretic) ≠ ordinary Model-Theoretic with default based proof theory • logic of fictions (Computer Science/AI, default based ) = Non-ordinary Model-Theoretic semantics; for example, Preference Model-Theoretic, others ≠ sole ordinary Model-Theoretic (because of the nature of fictions human should care)