Skip to main content

The Strength of Desires: A Logical Approach

Abstract

The aim of this paper is to propose a formal approach to reasoning about desires, understood as logical propositions which we would be pleased to make true, also acknowledging the fact that desire is a matter of degree. It is first shown that, at the static level, desires should satisfy certain principles that differ from those to which beliefs obey. In this sense, from a static perspective, the logic of desires is different from the logic of beliefs. While the accumulation of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tends to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while, in the positive view of desires developed here, one can argue that endorsing \(\varphi \vee \psi\) as a desire means to desire \(\varphi\) and to desire \(\psi\). However, desiring \(\varphi\) and \(\lnot \varphi\) at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire revision is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. While epistemic entrenchment relations are known to be qualitative necessity relations (in the sense of possibility theory), hedonic relations obeying a set of reasonable postulates correspond to another set-function in possibility theory, called guaranteed possibility, that drive well-behaved desire revision operations. Then the general framework of possibilistic logic provides a syntactic setting for encoding desire change. The paper also insists that desires should be carefully distinguished from goals.

This is a preview of subscription content, access via your institution.

Notes

  1. According to Dretske (1988), desire is also a necessary condition for reward. In particular, desire determines what counts as a reward for an agent. For example, a person can be rewarded with water only if she is thirsty and she desires to drink.

  2. This is an example where the logical disjunction symbol \(\vee\) should be read “and”, in natural language, as it translates into a set union, because the interpretations of \(\varphi\) understood as a desire are not mutually exclusive, contrary to when \(\varphi\) represents a belief. In the case where \(\varphi\) is a belief, the models of \(\varphi\) are mutually exclusive as candidates to be the real state of the world. So this set is a disjunction of situations, while if \(\varphi\) is a desire, any model of \(\varphi\) is a desirable situation, and the set of models of \(\varphi\) now collects all desirable situations, thus making the set of models a conjunction of situations. See Dubois and Prade (2012) and Zadeh (1978) for the importance of the distinction between the conjunctive and disjunctive interpretations of sets in another area.

  3. Remember that the set of models of \(\bot\) is \(\emptyset\).

  4. Called anhedonia as pointed out by a referee.

  5. As noticed by a referee.

  6. For simplicity, we assume that W does not contain unbearable interpretations.

  7. The term guaranteed comes from the fact that in possibility theory, \(\Delta (A) = 1\) means that all instances of A can actually be observed. It contrasts with potential possibility, which takes value 1 as soon as one instance of A is observed.

  8. This equality is the same as the one that Spohn ranking functions \(\kappa\) (Spohn 2012) satisfy, but identifying \(\Delta\) and \(\kappa\) would be misleading: \(\Delta\) and \(\kappa\) are antimonotonic with inclusion, but the ranges of \(\Delta\) and \(\kappa\), respectively [0, 1] and \({\mathbb {N}}\) (non-negative integers) are directed in opposite ways: \(\kappa ( A) = 0\) expresses full possibility, and the higher \(\kappa ( A)\) the more A is impossible, while \(\Delta (A) = 1\) expresses full possibility. When mapping \({\mathbb {N}}\) to [0, 1] via an order-reversing function (e.g., \(f(A) = 2^{-\kappa (A)})\), we obtain an increasing maxitive function: \(f(A\cup B) = \max (f(A),\, f(B))\), which departs from the characteristic property of \(\Delta\).

  9. Note that wine and cheese are complementary, while beer and wine can be viewed as redundant, and thus less jointly desirable.

  10. This distinction leads to the identification of two different kinds of moral dilemmas. The first kind of moral dilemma is the one which is determined by the logical conflict between two moral values. The paradigmatic example is the situation of a soldier during a war. As a member of the army, the soldier feels obliged to kills his enemies, if this is the only way to defend his country. But, as a catholic, he thinks that human life should be respected. Therefore, he feels morally obliged not to kill other people. The other kind of moral dilemma is the one which is determined by the logical conflict between desires and moral values. The paradigmatic example is that of Adam and Eve in the garden of Eden. They are tempted by the desire to eat the forbidden fruit and, at the same time, they have a moral obligation not to do it.

  11. At least this is so in the book (Gärdenfors 1988) as the epistemic entrenchment is a consequence of the axioms.

  12. In the paper, we use a very restrictive definition of epistemic entrenchment, which is the one in Gärdenfors (1988), that is, a total preorder relation on the language that obeys specific properties, which can only be justified if we take the two last AGM axioms for granted. Clearly one could envisage a less restrictive framework for desire revision, similar to the ones studied by Rott (2001) without (D*7) and (D*8).

References

  • Anscombe, G. E. M. (1957). Intention. Oxford: Basil Blackwell.

    Google Scholar 

  • Banerjee, M., & Dubois, D. (2014). A simple logic for reasoning about incomplete knowledge. International Journal of Approximate Reasoning, 55, 639–653.

    MathSciNet  Article  MATH  Google Scholar 

  • Benferhat, S., Dubois, D., Kaci, S., & Prade, H. (2002). Bipolar possibilistic representations. In A. Darwiche & N. Friedman (Eds.), Proceedings of the 18th conference in uncertainty in artificial intelligence (UAI ’02) (pp. 45–52). Edmonton, Alberta: Morgan Kaufmann.

    Google Scholar 

  • Benferhat, S., Dubois, D., Kaci, S., & Prade, H. (2006). Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions. Information Fusion, 7, 135–150.

    Article  Google Scholar 

  • Benferhat, S., Dubois, D., & Prade, H. (1999). Towards a possibilistic logic handling of preferences. In Proceedings of the 16th conference on artificial intelligence (IJCAI 99) (pp. 1370–1375). Stockholm: Morgan Kaufmann.

  • Benferhat, S., Dubois, D., & Prade, H. (2001). A computational model for belief change and fusing ordered belief bases. In M.-A. Williams & H. Rott (Eds.), Frontiers in belief revision (pp. 109–134). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Benferhat, S., Dubois, D., Prade, H., & Williams, M.-A. (2002). A practical approach to revising prioritized knowledge bases. Studia Logica, 70, 105–130.

    MathSciNet  Article  MATH  Google Scholar 

  • Benferhat, S., & Kaci, S. (2003). Logical representation and fusion of prioritized information based on guaranteed possibility measures: Application to the distance-based merging of classical bases. Artificial Intelligence, 148(1–2), 291–333.

    MathSciNet  Article  MATH  Google Scholar 

  • Bonanno, G. (2009). Rational choice and AGM belief revision. Artificial Intelligence, 173(12–13), 1194–1203.

    MathSciNet  Article  MATH  Google Scholar 

  • Boutilier, C. (1993). Revision sequences and nested conditionals. In Proceedings of the 13th international joint conference on artificial intelligence (IJCAI’93) (pp. 519–525). Chambéry: Morgan Kaufmann.

  • Casali, A., Godo, L., & Sierra, C. (2011). A graded BDI agent model to represent and reason about preferences. Artificial Intelligence, 175, 1468–1478.

    MathSciNet  Article  MATH  Google Scholar 

  • Castelfranchi, C., & Paglieri, F. (2007). The role of beliefs in goal dynamics: Prolegomena to a constructive theory of intentions. Synthese, 155(2), 237–263.

    MathSciNet  Article  Google Scholar 

  • Doyle, J., Shoham, Y., & Wellman, M. P. (1991). A logic of relative desire (preliminary report). In Z. Ras & M. Zemankova (Eds.), Methodologies for intelligent systems (ISMIS 1991), lecture notes in computer science (Vol. 542, pp. 16–31). New York: Springer.

    Google Scholar 

  • Dretske, F. (1988). Explaining behavior: Reasons in a world of causes. Cambridge: MIT Press.

    Google Scholar 

  • Dubois, D. (1986). Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence (Bratislava), 5(6), 403–416.

    MATH  Google Scholar 

  • Dubois, D., Hajek, P., & Prade, H. (2000). Knowledge-driven versus data-driven logics. Journal of logic, Language and information, 9, 65–89.

    MathSciNet  Article  MATH  Google Scholar 

  • Dubois, D., Lorini, E., & Prade, H. (2013). Bipolar possibility theory as a basis for a logic of desires and beliefs. In W. Liu, V. S. Subrahmanian, & J. Wijsen (Eds.), Proceedings of the 7th international conference scalable uncert. Mgmt. (SUM’13), LNCS 8078. Washington, DC: Springer.

    Google Scholar 

  • Dubois, D., Lorini, E., & Prade, H. (2014). Nonmonotonic desires–A possibility theory viewpoint. In R. Booth, G. Casini, S. Klarman, G. Richard, & I. J. Varzinczak (Eds.), Proceedings of the international workshop on defeasible and ampliative reasoning (DARe@ECAI 2014) (Vol. 1212). Prague: CEUR Workshop Proceedings.

    Google Scholar 

  • Dubois, D., Lorini, E., & Prade, H. (2015). Revising desires–A possibility theory viewpoint. In T. Andreasen, H. Christiansen, J. Kacprzyk, H. Larsen, G. Pasi, O. Pivert, G. De Tré, M. A. Vila, A. Yazici, & S. Zadrożny (Eds.), Proceedings of the 11th international conference on flexible query answering systems (FQAS’15) (Vol. 400, pp. 3–13). Advances in Intelligent Systems and Computing series.

  • Dubois, D., Lorini, E., & Prade, H. (2016). A possibility theory-based approach to desire change. In R. Booth, G. Casini, S. Klarman, G. Richard, & I. J. Varzinczak (Eds.), Proceedings of the international workshop on defeasible and ampliative reasoning (DARe@ECAI 2016) (Vol. 1626). The Hague: CEUR Workshop Proceedings.

    Google Scholar 

  • Dubois, D., & Prade, H. (1991). Epistemic entrenchment and possibilistic logic. Artificial Intelligence, 50, 223–239.

    MathSciNet  Article  MATH  Google Scholar 

  • Dubois, D., & Prade, H. (1992). Belief change and possibility theory. In P. Gärdenfors (Ed.), Belief revision (pp. 142–182). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Dubois, D., & Prade, H. (1998). Possibility theory: Qualitative and quantitative aspects. In D. Gabbay & P. Smets (Eds.), Quantified representation of uncertainty and imprecision, handbook of defeasible reasoning and uncertainty management systems (Vol. 1, pp. 169–226). Dordrecht: Kluwer.

    Google Scholar 

  • Dubois, D., & Prade, H. (2004). Possibilistic logic: A retrospective and prospective view. Fuzzy Sets and Systems, 144, 3–23.

    MathSciNet  Article  MATH  Google Scholar 

  • Dubois, D., & Prade, H. (2009a). Accepted beliefs, revision and bipolarity in the possibilistic framework. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief (pp. 161–184). New York: Springer.

    Chapter  Google Scholar 

  • Dubois, D., & Prade, H. (2009b). An overview of the asymmetric bipolar representation of positive and negative information in possibility theory. Fuzzy Sets and Systems, 160(10), 1355–1366.

    MathSciNet  Article  MATH  Google Scholar 

  • Dubois, D., & Prade, H. (2012). Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets. Fuzzy Sets and Systems, 192, 3–24.

    MathSciNet  Article  MATH  Google Scholar 

  • Gärdenfors, P. (1988). Knowledge in flux. Modeling the dynamics of epistemic states. Cambridge: The MIT Press.

    MATH  Google Scholar 

  • Gärdenfors, P. (1990). Belief revision and nonmonotonic logic: Two sides of the same coin? In Proceedings of the 9th European conference on artificial intelligence (ECAI’90) (pp. 768–773). Stockholm.

  • Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17, 157–170.

    MathSciNet  Article  MATH  Google Scholar 

  • Harsanyi, J. (1955). Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy, 63, 309–321.

    Article  Google Scholar 

  • Harsanyi, J. (1982). Morality and the theory of rational behaviour. In A. K. Sen & B. Williams (Eds.), Utilitarianism and beyond. Cambridge: Cambridge University Press.

    Google Scholar 

  • Humberstone, I. L. (1992). Direction of fit. Mind, 101(401), 59–83.

    Article  Google Scholar 

  • Hume, D. (1978). A treatise of human nature (2nd Oxford edn.). L. A. Selby-Bigge & P. H. Nidditch (Eds.), Oxford: Oxford University Press.

  • Lang, J., & van der Torre, L. (1996). Conditional desires and utilities: An alternative logical approach to qualitative decision theory. In W. Wahlster (Ed.), Proceedings of the 12th European conference artificial intelligence (ECAI’96) (pp. 318–322). Budapest: Wiley .

    Google Scholar 

  • Lang, J., & van der Torre, L. (2008). From belief change to preference change. In M. Ghallab, C. D. Spyropoulos, N. Fakotakis, & N. M. Avouris (Eds.), Proceedings of the 18th European conference on artificial intelligence (ECAI’08) (pp. 351–355). Patras: IOS Press.

    Google Scholar 

  • Lang, J., van der Torre, L., & Weydert, E. (2002). Utilitarian desires. Journal of Autonomous Agents and Multi-Agent Systems, 5, 329–363.

    Article  Google Scholar 

  • Lang, J., van der Torre, L., & Weydert, E. (2003). Hidden uncertainty in the logical representation of desires. In G. Gottlob & T. Walsh (Eds.), Proceedings of the 18th international joint conference on artificial intelligence (IJCAI’03) (pp. 685–690). Acapulco: Morgan Kaufmann.

    Google Scholar 

  • Lewis, D. (1973). Counterfactuals and comparative possibility. Journal of Philosophical Logic, 2(4), 418–446.

    MathSciNet  Article  MATH  Google Scholar 

  • Locke, J. (1975). An essay concerning human understanding. Oxford: Oxford University Press. The Clarendon Edition of the Works of John Locke.

    Google Scholar 

  • Lorini, E. (2014). A logic for reasoning about moral agents. Logique et Analyse, Centre National de Recherches en Logique (Belgium), 58(230), 177–218 .

    MathSciNet  Google Scholar 

  • Platts, M. (1979). Ways of meaning. London: Routledge and Kegan Paul.

    Google Scholar 

  • Rao, A. S., & Georgeff, M. P. (1991). Modeling rational agents within a BDI-architecture. In Proceedings of the 2nd international conference on principles of knowledge representation and reasoning (pp. 473–484).

  • Rott, H. (2001). Change, choice and inference. A study of belief revision and nonmonotonic reasoning. Oxford: Clarendon Press.

    MATH  Google Scholar 

  • Schroeder, T. (2004). Three faces of desires. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Searle, J. (1979). Expression and meaning. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Searle, J. (2001). Rationality in action. Cambridge: MIT Press.

    Google Scholar 

  • Spohn, W. (2012). The laws of belief: Ranking theory and its philosophical applications. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323.

    Article  MATH  Google Scholar 

  • van Benthem, J., Girard, P., & Roy, O. (2009). Everything else being equal: A modal logic for ceteris paribus preferences. Journal of Philosophical Logic, 38, 83–125.

    MathSciNet  Article  MATH  Google Scholar 

  • van Benthem, J., & Liu, F. (2007). Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics, 17(2), 157–182.

    MathSciNet  Article  MATH  Google Scholar 

  • Von Wright, G. H. (1963). The logic of preference. Edinburgh: Edinburgh University Press.

    Google Scholar 

  • Von Wright, G. H. (1972). The logic of preference reconsidered. Theory and Decision, 3, 140–169.

    Article  MATH  Google Scholar 

  • Zadeh, L. A. (1978). PRUF: A meaning representation language for natural languages. International Journa of Man-Machine Studies, 10, 395–460.

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the referees for a careful reading and insightful remarks, that led us to clarify a number of issues in the paper, in particular, the shaping of the proof of the completeness Theorem 1.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Henri Prade.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dubois, D., Lorini, E. & Prade, H. The Strength of Desires: A Logical Approach. Minds & Machines 27, 199–231 (2017). https://doi.org/10.1007/s11023-017-9426-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11023-017-9426-5

Keywords

  • Desire
  • Revision
  • Possibility theory