Logic of Fiction and Logic in Computer Science

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Logic of Fiction and Logic in Computer Science

• Chayunt Mathon
• Department of Philosophy, Chulalongkorn
  University
• Thailand

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Fictions

• Fictional Discourse
• Fictive Discourse
• Metafictive Discourse
• Transitive Discourse

• Theories of Fiction
• Ontological Analysis
• Fictive-operator Analysis
• Pretense, Imagination, and Make Believe Analysis

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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 authors 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 authors 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.

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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.

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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-s
  tories that Sherlock Holmes was a detective. The
  exemplars are
• ? Possible world analyses (Plantinga, 1974 and
  Kaplan, 1973 and Gabriel, 1979 andLewis,
  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-quantificationa
  l 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.

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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 Searls 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.

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Nature of Fictions

• A fiction is a made-up story. (Scholes, Robert
  (1991) Element of Literature)
• Theres no one right way to read a piece of
  fiction. There are many good ways. This does not
  mean that anyones reading of a piece of fiction
  is equal to anyone elses. 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 )

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Structure of Formal logical System

• Grammar formal Language/symbols
• Deductive Apparatus axiom(s)/ Rules of Inference
• ? Proof Theory
• Semantics Interpretations of formal language

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Historical sematics approach of Logic of Fiction

• We, intuitively, can valuate a metafictive
  proposition to 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 so or the author say so.

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Historical systematic approach to the 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

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

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

• Take the ordinary Model-Theoretic Semantics.
• 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 speakers common knowledge

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Monotonic-Nonmonotonic Logics

• Monotonic Logic
• - Aristotelian logic
• - Classical logic
• - deal only with patterns of inference that hold
  without exception

• Nonmonotonic Logics
• - It is reasonable to ignore outlandish
  possibilities.

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Default based logic

• To ignore outlandish possibilities is 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.

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Recall

• (Clayton, John J. (2000) The Heath Introduction
  to Fiction )
• Theres no one right way to read a piece of
  fiction. There are many good ways. This does not
  mean that anyones reading of a piece of fiction
  is equal to anyone elses. 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.

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AND

• Need of ordinary Model-Theoretic

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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)

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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)

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