PI: Dr. Dr. Momme von Sydow
Institution: Ruprecht-Karls-Universität Heidelberg
Abstract
This research proposal aims to contribute to the development (and convergence) of Bayes Logic (BL) and Bayes Nets (BN), as well as a more unified understanding of the rationality underlying probabilistic logical and causal predications. Bayes logic is a recent normative and descriptive model of the induction of noisy-logical relationships that provides a refined probabilistic adequacy criterion for predication as well as a coherent account of Bayesian non-monotonic belief-update of assertive (dyadic) propositions. BL postulates that people often employ probabilities of hypotheses about noisy-logical propensities characterizing a whole situation in a single sentence (probabilities of logical probability patterns), rather than probabilities of specific subsets alone (extensional probabilities). BL may explain both the psychological logic of frequency-based conjunction fallacies and an important class of human probability judgments in general. This "psycho-logic" deviates from the standard "narrow norm" of standard (extensional) probability. It is argued that using this "narrow norm" to formalize a high probability-criterion for predication leads to several fundamental problems. For example, using this narrow norm the judgment "P(ravens are black AND they can fly) > P(ravens are black OR they can fly or both)" is fallacious (a 'conjunction fallacy' or more generally an 'inclusion fallacy'): A Ù B is clearly a subset of A Ú B (i.e., logically, A Ù B ⇒ A Ú B). This seems to hold true, even independently of empirical evidence. Nevertheless, actual predications appear dependent upon evidence in a reasonable way, thus actual judgments differ from the "narrow norm". (In fact, most people find the latter sentence "less probably valid".) An adequacy criterion of predication should be reliant on (empirical) data. BL has fared well, predicting systematic inclusion fallacies based on qualitative and quantitative manipulations, including the conditions of double CFs, sample size effects, and pattern sensitivity effects. Finally, BL has usefully generalized the concept of conjunction fallacies to address other logical connectives. Bayes Nets and closely related inductive models (e.g., Delta P, Power PC, and causal support) have been developed in recent decades in the fields of philosophy, AI, and psychology, to represent probabilistic conditional dependencies and independencies in acyclical directed causal graphs. Causal BNs (or models). This probabilistic representation improves on traditional psychological accounts, such as Mental Models or Mental Logics. Nevertheless, linked to the Markov assumption, these representations do not normally involve probabilistic logical relationships referring to the use of logical terms in language (they do not even account for non-causal conditionals). In the outlined research project I build upon the fruitful aspects of BL and BN, which provide complementary contributions to the probabilistic understanding of induction and reasoning. I will investigate noisy-logical induction, predications, probability judgments and reasoning in causal and non-causal scenarios. BL provides significant new contribution to these issues and a general account of frequency-based inclusion fallacies that are interpreted to be rational. BL provides a rational model of noisy-logical predication that should be tested in the context of causal networks. However, these predicates are not causal. Additionally here a Causal Bayesian Logic (CBL) is proposed, that provides an account of causal noisy-logical relationships and substantially extends the probabilistic causal approach of BN, not accounting for such relationships. Hence, BL (and its causal extension) add noisy-logical relationships (causal and non-causal ones) to BNs, in order to build a more unified, but still domain-sensitive, understanding of probabilistic logical and causal representation, induction and reasoning.
Project-related Publications
Hebbelmann, D., & von Sydow, M (2014). Betting on transitivity in an economic setting. In Proceedings of the 36th Annual Meeting of the Cognitive Science Society (pp. 2339-2344). Austin, TX: Cognitive Science Society.
More publications can be found on this page.
Institution: Ruprecht-Karls-Universität Heidelberg
Abstract
This research proposal aims to contribute to the development (and convergence) of Bayes Logic (BL) and Bayes Nets (BN), as well as a more unified understanding of the rationality underlying probabilistic logical and causal predications. Bayes logic is a recent normative and descriptive model of the induction of noisy-logical relationships that provides a refined probabilistic adequacy criterion for predication as well as a coherent account of Bayesian non-monotonic belief-update of assertive (dyadic) propositions. BL postulates that people often employ probabilities of hypotheses about noisy-logical propensities characterizing a whole situation in a single sentence (probabilities of logical probability patterns), rather than probabilities of specific subsets alone (extensional probabilities). BL may explain both the psychological logic of frequency-based conjunction fallacies and an important class of human probability judgments in general. This "psycho-logic" deviates from the standard "narrow norm" of standard (extensional) probability. It is argued that using this "narrow norm" to formalize a high probability-criterion for predication leads to several fundamental problems. For example, using this narrow norm the judgment "P(ravens are black AND they can fly) > P(ravens are black OR they can fly or both)" is fallacious (a 'conjunction fallacy' or more generally an 'inclusion fallacy'): A Ù B is clearly a subset of A Ú B (i.e., logically, A Ù B ⇒ A Ú B). This seems to hold true, even independently of empirical evidence. Nevertheless, actual predications appear dependent upon evidence in a reasonable way, thus actual judgments differ from the "narrow norm". (In fact, most people find the latter sentence "less probably valid".) An adequacy criterion of predication should be reliant on (empirical) data. BL has fared well, predicting systematic inclusion fallacies based on qualitative and quantitative manipulations, including the conditions of double CFs, sample size effects, and pattern sensitivity effects. Finally, BL has usefully generalized the concept of conjunction fallacies to address other logical connectives. Bayes Nets and closely related inductive models (e.g., Delta P, Power PC, and causal support) have been developed in recent decades in the fields of philosophy, AI, and psychology, to represent probabilistic conditional dependencies and independencies in acyclical directed causal graphs. Causal BNs (or models). This probabilistic representation improves on traditional psychological accounts, such as Mental Models or Mental Logics. Nevertheless, linked to the Markov assumption, these representations do not normally involve probabilistic logical relationships referring to the use of logical terms in language (they do not even account for non-causal conditionals). In the outlined research project I build upon the fruitful aspects of BL and BN, which provide complementary contributions to the probabilistic understanding of induction and reasoning. I will investigate noisy-logical induction, predications, probability judgments and reasoning in causal and non-causal scenarios. BL provides significant new contribution to these issues and a general account of frequency-based inclusion fallacies that are interpreted to be rational. BL provides a rational model of noisy-logical predication that should be tested in the context of causal networks. However, these predicates are not causal. Additionally here a Causal Bayesian Logic (CBL) is proposed, that provides an account of causal noisy-logical relationships and substantially extends the probabilistic causal approach of BN, not accounting for such relationships. Hence, BL (and its causal extension) add noisy-logical relationships (causal and non-causal ones) to BNs, in order to build a more unified, but still domain-sensitive, understanding of probabilistic logical and causal representation, induction and reasoning.
Project-related Publications
Hebbelmann, D., & von Sydow, M (2014). Betting on transitivity in an economic setting. In Proceedings of the 36th Annual Meeting of the Cognitive Science Society (pp. 2339-2344). Austin, TX: Cognitive Science Society.
More publications can be found on this page.