**The Modal Logic in the Narrative and the Natural Language**

**1 ****Preliminaries**

**1.1 **** Introduction**

The revival of the modal logic studies in the 1950s has echoed in both narratology and linguistics. At first, in the narratology, Algirdas Julien Greimas (1966) noticed that the logical elements of the plot, as they were specified by Vladimir Propp (1928/1963) and some others after him are, in fact, modalities. Then, John Lyons (1978) identified as logical modalities some properties of the language. Both Greimas and Lyons were especially influenced, first of all, by Georg Henrik von Wright (1951) with his analysis of the alethic, deontic, and epistemic modalities.

Then, in the narratology, Lubomir Doležel (1976; 1998) proposed the first systematic review of the modalities used in the construction of the fictional plot. Independently, Frank Ankersmith (1983), following some ideas of Arthur Danto (1965), discovered the role of the modal logics in the historiography. In the same time, Paul Ricœur (1984-1985) argued for the “grande narratologie” that includes both fiction and historiography. Finally, in the studies of the syntax of natural languages, Guglielmo Cinque (1999) described a system of “functional heads” whose meaning is identified as modal by Cinque himself, while only for a part of them. It seems to me, however, that Cinque describes as a whole the system of logical modalities which can be expressed in the syntax structures, which has been previously fragmentary detected by Lyons. However, this Cinque’s system has never been studied from a logical point of view.

This system of Cinque’s linguistic modalities has striking similarity with that of the narratology. Without being able to explore Cinque’s argumentation at length, I would prefer to describe the modalities of the narratology and to pose them alongside with Cinque’s system.

**1.2. **** Logical modalities: definition and interpretations**

The discussion of the problem of modalities in the narratology and the linguistics suffers from a vagueness of terminology and concepts. Therefore, we have to start from the definitions of the basic terms.

“Ask three modal logicians what modal logic is, and you are likely to get at least three different answers.” (Blackburn *et al.* 2002, viii). Indeed, it is difficult to find out a definition of the very notion of “modality.” Very often, it is introduced in an intuitive way or within a mathematical formalism, in both cases without any explicit connection to the other branches of logics and philosophy. Of course, there are other approaches. Among them, the most popular is the interpretation of “modality” as a state of things in some of the possible worlds. However, the semantics of possible worlds, being a powerful tool of making clear the meaning of the alethic and some other modalities, turns out to be an obstacle in understanding of other modalities, *e.g.*, spatial (cf. (von Wright 1979)). This is one of the (many!) causes which make desirable to present the modal logic with no relation to the semantics of possible worlds and within the context of other (classical) logical systems.

Alternatively to the possible worlds approach, the modal logics can be presented as particular cases of classical logic. The main line of reasoning is the following (Blackburn *et al.* 2002; 2006). The basic notion is that of “relational structure” that is defined as a set together with collection of relations on that set. Obviously, such structures are to be found everywhere. The relational structures could be approached from an external viewpoint, as normally the modern scholarship does, and this will be the objectivist, so-to-say, approach used by classical logic. Alternatively, the relational structures could be approached from an internal viewpoint, from within. This way of observation where the presence of the observer himself is implied is that of modal logic. Thus, “... modal languages talk about relational structures in a special way: 'from the inside' and 'locally.' Rather than standing outside a relational structure and scanning the information it contains from some celestial vantage point, modal formulas are evaluated *inside* structures, at *a particular state*. The function of the modal operators is to permit the information stored at other states to be scanned — but, crucially, *only the states accessible from the current point via an appropriate transition may be accessed in this way*. <...> the reader who pictures a modal formula as a little automaton standing at some state in a relational structure, and only permitted to explore the structure by making journeys to neighboring states, will have grasped one of the key intuitions of modal model theory.” (Blackburn *et al.* 2002, ix).

From this perspective, “...modal logic can be regarded as a fragment of first- and second-order classical logic.” (*Ibid.*, xi). What we are the most interested in, however, is an evident usability of modal logic in interpretation of both thinking process itself and its resulting activities such as discourse (that produces narratives) and language.

To sum up, one can say that modal logic considers the *states* of relational systems from an insider point of view.

**1.3. **** Modal logic approach in the cognitive science**

The number of states that are discernible from some internal viewpoint is unlimited. Moreover, any kind of modal logic can be combined with some another and/or a kind of classical logical reasoning. As a result, the number of possible modal logical systems is infinite. Dealing with a given kind of problems, that is, with a given kind of relational systems, we have to choose only the appropriate kinds of logical reasoning.

Thus, it is *a priori* likely that the number of logical modes of the psychological process of human thinking is far from being unlimited. It is likely that human thinking operates with a limited number of elementary logical modalities to be able to understand any other modalities that it is able to understand. These modes are natural logical tools given to the human cognitive sphere to work. However, so far, no study of the logical modalities of the human cognitive sphere is performed.

The studies of natural language’s syntax and structure of narrative are two of the most natural areas where such study might be initiated. Some congruency of the modal logic systems at work in both would be not to wonder and could be explained by some mechanisms of the human thinking as such. In this way, the studies of modalities of narratology and syntax are both means of investigation of the human cognitive sphere.

Here, I shall limit myself to a review of application of the modal logic approach to the narratology with remarks on the possible use of this approach in the theoretical linguistics, especially in the light of Cinque’s treatment of the functional heads.