Quasi Conjunction, Quasi Disjunction, T-norms and T-conorms: Probabilistic Aspects

We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on $n$ conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical dependencies, and we study the relations among coherence, inclusion for conditional events, and p-entailment. We also consider the Or rule, where quasi conjunction and quasi disjunction of premises coincide with the conclusion. We analyze further aspects of quasi conjunction and quasi disjunction, by computing probabilistic bounds on premises from bounds on conclusions. Finally, we consider biconditional events, and we introduce the notion of an $n$-conditional event. Then we give a probabilistic interpretation for a generalized Loop rule. In an appendix we provide explicit expressions for the Hamacher t-norm and t-conorm in the unitary hypercube

Constraint rule-based programming of norms for electronic institutions

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Collective Intentionality

In this chapter, we focus on collective action and intention, and their relation to conventions, status functions, norms, institutions, and shared attitudes more generally. Collective action and shared intention play a foundational role in our understanding of the social. The three central questions in the study of collective intentionality are: (1) What is the ontology of collective intentionality? In particular, are groups per se intentional agents, as opposed to just their individual members? (2) What is the psychology of collective intentionality? Do groups per se have psychological states, in particular propositional attitudes? What is the psychology of the individuals who participate in collective intentional behavior? What is special about their participatory intentions, their we-intentions, as they are called (Tuomela and Miller 1988), as opposed to their I-intentions? (3) How is collective intentionality implicated in the construction of social reality? In particular, how does the content of we-intentions and the intentional activity of individual agents create social institutions, practices and structures? We first discuss collective action and shared intention in informal groups. Next we discuss mechanisms for constructing institutional structures out of the conceptual and psychological resources made available by our understanding of informal joint intentional action. Then we extend the discussion of collective action and intention to institutional groups, such as the Supreme Court, and explain how concepts of such organizations are constructed out of the concepts of a rule, convention, and status function. Finally we discuss collective attitudes beyond intention

Counterfactual Skepticism and Multidimensional Semantics

It has recently been argued that indeterminacy and indeterminism make most ordinary counterfactuals false. I argue that a plausible way to avoid such counterfactual skepticism is to postulate the existence of primitive modal facts that serve as truth-makers for counterfactual claims. Moreover, I defend a new theory of ‘might’ counterfactuals, and develop assertability and knowledge criteria to suit such unobservable ‘counterfacts’

Quantum-like models cannot account for the conjunction fallacy

Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities—this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed