Propositional Attitudes in Non-Compositional Logic

Several authors analyzed propositional attitudes (wish, fear, regret, glad) by integrating their epistemic and deontic components. This paper extends previous work done by the author and presents a logical calculus inspired by Possibility Theory, a non-compositional version of fuzzy logic. Linguistic properties of glad, regret, wish, fear Fact 1: The factual predicates glad and regret presuppose the agent’s knowledge of the propositional content (Kiparsky & Kiparsky, 1971). Situations that cannot be known cannot be object of these attitudes. (1) a. I’m so glad that he will return in episode seven. b. #Joan is glad that she will win the Texas lottery scratchcard jackpot (Telegraph, 13 Aug 2011). (2) a. You regret that he will move to Singapore. b. #He regrets that there is an earthquake tomorrow. Fact 2: The predicates wish and fear presuppose the agent’s lack of knowledge of the propositional content (Gerner 2010a). Events that are known to happen cannot be object of wishes and fears. (3) a. I wish that you’d grow up. b. #I wish that I will get married tomorrow. (4) a. Syria’s neighbors fear that fighting could spread. b. #John fears that he has an elder brother. Fact 3: No agent who is right in his mind can wish or be glad about events that he values as bad. In the same vein, no event that is rated positively in the value system of a human agent can be regretted or feared by him. (5) a. #The president was glad that his words had been misinterpreted. b. #Bill regrets that a solution to his problems exists. (6) a. #The king wished that the royal wedding would be spoiled by riots. b. #I fear that someone, somewhere, may be happy. Constraints: These facts about attitudinal predicates can be captured by Searle-style preparatory and propositional conditions (Searle, 1969, 1979; Gerner, 2010a,b,c). Preparatory Propositional glad the agent knows φ based on background information φ is not bad in the value system of a human agent regret the agent knows φ based on background information φ is not good in the value system of a human agent wish the speaker does not know φ based on background information φ is not bad in the value system of a human agent fear the speaker does not know φ based on background information φ is not good in the value system of a human agent The logic of propositional attitudes Propositional attitudes like glad, regret, wish, fear have epistemic and deontic components (Heim, 1992; Gerner, 2010a,b,c). The computation of these components can be modeled by necessity/possibility measures in the sense of Possibility Theory (Dubois & Prade, 1988; 2001). Let SENT be the set of Boolean propositions and let the following epistemic and deontic modalities be given: NESS, POSS, OBLI, PERM: SENT  {0, 1} such that NESS (epistemic) and OBLI (deontic) are two necessity measures, and POSS (epistemic) and PERM (deontic) two possibility measures. We can capture the agent’s epistemic state and deontic state of φ ∈ SENT in the following way (Dubois & Prade, 2001: 40): Copyright © 2012, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. 295 Proceedings of the Twenty-Fifth International Florida Artificial Intelligence Research Society Conference