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The cognitive structure of surprise: looking for basic principles

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Abstract

We develop a conceptual and formal clarification of notion of surprise as a belief-based phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of cognitive processing and involves particular kinds of epistemic representations (representations and expectations under scrutiny, implicit beliefs, presuppositions). We define two main kinds of surprise: mismatch-based surprise and astonishment. In the central part of the paper we suggest how a formal model of surprise can be integrated with a formal model of belief change. We investigate the role of surprise in triggering the process of belief reconsideration. There are a number of models of surprise developed in the psychology of emotion. We provide several comparisons of our approach with those models.

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Notes

  1. The necessity for a distinction between a mere activity of seeing, hearing, smelling something and a complex cognitive activity of perceptual recognition of an object or event has also been stressed by Dretske (1981).

  2. In the extended version of this paper (Lorini and Castelfranchi 2006a) we investigate also those forms of surprise due to the invalidation of the agent’s presupposed frame. We provide a general definition of frame (or script) as agglomerate of conditional beliefs and argue that a special kind of surprise (called disorientation) arises from the invalidation and revision of the conditional beliefs which are part of a given presupposed frame of the agent.

  3. We use the term “informational mental state” in order to distinguish it from a “motivational mental state” (a desire, intention, wish, goal and so on).

  4. Notice that “to feel surprised” should not be confused with “having awareness of our own surprise” (for a distinction between phenomenal consciousness and access consciousness see Bloch 1995; Chalmers 1995).

  5. The need for the distinction between data and beliefs has been addressed by several other authors (see Paglieri 2004 on this). For instance Tamminga (2001) advocated the need for two levels of explanation in dealing with belief revision, namely information (data) and beliefs. This leads him to describe belief revision as a two step process: first, information revision, managed by applying a paraconsistent monotonic logic of first-degree entailment; second, belief extraction, that takes care of assuring nonmonotonicity, consistency, and closure under logical consequence. In Tamminga’s work, the main focus is placed on inconsistency at the level of information (data) vs. consistency at the level of beliefs.

  6. Our test function is comparable to the awareness function defined in Fagin and Halpern (1987).

  7. (a) All instances of propositional tautologies; (b) Modus ponens: from \({\vdash\Phi}\) and Φ→Ψ infer Ψ; (c) K-axiom for \({Bel: Bel(\Phi\rightarrow\Psi)\wedge Bel\Phi\rightarrow Bel\Psi}\) ; (d) Bel-Necessitation: From \({\vdash\Phi}\) infer \({\vdash Bel\Phi}\).

  8. (a) Nonnegativity: \({P(\varphi)\geq 0}\); (b) Probability of Truth: \({P(\top)=1}\) ; (c) Additivity: \({P(\Phi_{1}\wedge\Phi_{2})+P(\Phi_{1}\wedge\neg\Phi_{2})=P(\Phi_{1})}\); (d) Equivalence: From \({\vdash\Phi_{1}\longleftrightarrow\Phi_{2}}\) infer \({\vdash P(\Phi_{1})=P(\Phi_{2})}\) .

  9. See Fagin and Halpern (1994).

  10. There is considerable emprical evidence showing that in being active and available at an automatic and effortless level background (passive) expectations can affect subject’s performances and judgments and can conflict with conscious (scrutinized) expectations (on this see Matt et al. 1992; Sommer et al. 1998).

  11. Formal proofs of theorems, lemmas and propositions are given in an extended version of this paper (Lorini and Castelfranchi 2006a).

  12. See for instance Hansson (1999) for a complete account of belief revision applied to belief bases.

  13. Obviously we assume that the expectation under scrutiny is a special kind of explicit belief (see Fig. 1).

  14. As noticed in the previous section it could also be a probabilistic inference (a post-hoc reconstruction of the probability of the perceived fact).

  15. At a meta-level too we might say that the mismatch was unexpected.

  16. The same criticism can be addressed to all those computational models which claim that surprise is simply a function of unexpectedness of the incoming input and which neglect the dimension strength of the invalidated expectation (Macedo and Cardoso 2001; Meyer et al. 1997; Ortony and Partridge 1987). Other models based on information theory claim that surprise is a function of the distance between prior probabilities and posterior probabilities after the conditioning on the set of perceived data (see Baldi 2004 for instance). For the same reasons we believe that this last approach is incomplete since it is unable to provide qualitative distinctions inside the surprise phenomenon.

  17. Richer logics of information update have been proposed. In Baltag et al.’s logic of information update (Baltag et al. 1998) for instance complex communicative actions are described in terms of action models, which stand for complex events that carry information for agents. Different kinds of informational scenarios in a multi-agent setting can be described in this logic. For instance, we can describe scenarios where not all agents have the same observational access to what is happening in reality. In van Benthem et al. (2006) probabilities are added to Baltag et al.’s framework in order to reason about probabilistic information in a multi-agent setting and to describe how belief and probability update is affected by the reliability of the source of information.

  18. We generalise here the standard approach of dynamic logic where actions are interpreted as transitions between worlds in a model (see also van Linder et al. 1997; Meyer et al. 1999). Indeed we interpret update processes as transitions between pairs (model, world).

  19. This assumption is made in order to avoid dividing by zero (Condition 2c in Definition 6) when redefining the probability function after an update with a sentence with probability zero. More general approaches to updating with sentences with probability zero are discussed in Halpern (2001, 2003).

  20. For belief revision with inconsistent information see for instance Herzig and Longin (2002) and van Benthem (2006).

  21. The same result is obtained in Kooi (2003).

  22. This postulate corresponds to the following semantic constraint: for every \(w\in W \hbox{ if } {R^{\varphi!}(M,w)\neq\emptyset} \hbox{ then }\varphi=DATA(w).\)

  23. Given the definition \({Background(\varphi)=_{def}\left\langle retrieve(\varphi)\right\rangle \top}\) and property (Perc 1) of perceptual actions (see Sect. 2.3) we can express the semantics corresponding to this principle by the following first order formula: for every \(w\in W \hbox{ if }{R^{\varphi!}(M,w)\neq\emptyset}\) and TEST(w) = ψ and there is a w′ such that w′∈B(w) and \({R_{1}^{observe(\varphi)}(w')\neq\emptyset}\) and \({R_{1}^{observe(\psi)}(w')\neq\emptyset}\) then \({R_{2}^{retrieve(\varphi)}(w')\neq\emptyset}\) or \({R_{2}^{retrieve(\neg\varphi)}(w')\neq\emptyset}\).

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Acknowledgments

We are very grateful to Johan van Benthem and to the anonymous referees of this paper for their helpful comments on the content of our work. Our research has been supported by the European Project “MindRACES: from Reactive to Anticipatory Cognitive Embodied Systems” (IST-511931).

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  1. Institute of Cognitive Sciences and Technologies-CNR, Via San Martino della Battaglia 44, 00185, Rome, Italy

    Emiliano Lorini & Cristiano Castelfranchi

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  1. Emiliano Lorini
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Correspondence to Cristiano Castelfranchi.

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Lorini, E., Castelfranchi, C. The cognitive structure of surprise: looking for basic principles. Topoi 26, 133–149 (2007). https://doi.org/10.1007/s11245-006-9000-x

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