## 24th July 2017Bristol. Howard House, 4th floor seminar room. Organised by Can Baskent. Contact Can or Catrin with any questions. 1445: Walter Carnielli - Consistency, possibilistic, and necessitistic measures 1530: Break 1545: Rohit Parikh - An Epistemic Generalization of Rationalizability 1630: End ## Abstracts## Consistency, possibilistic, and necessitistic measuresCentre for Logic, Epistemology and the History of Science and Department of Philosophy State University of Campinas- Unicamp Possibility and necessity theories rival with probability in
representing uncertain knowledge, while offering a more qualitative
view of uncertainty. Moreover, necessity and possibility measures
constitute, respectively, lower and upper bounds for probability
measures, with the advantage of avoiding the complications of the
notion of probabilistic independence. On the other hand, paraconsistent formal systems, especially the
Logics of Formal Inconsistency, are capable of quite carefully
expressing the circumstances of reasoning with contradictions. In
connection to this, a calculus for reasoning with conflicting
evidence, LETj, was proposed by (Carnielli & Rodrigues 2016). The aim
of this talk is to merge these ideas, by precisely defining new
notions of possibility and necessity theories involving the concept of
consistency (inspired in (Besnard & Lang 1994)) based on the
paraconsistent and paracomplete logic Cie, connecting them to the
notion of partial and conclusive evidence. This will also work as an
attempt to fill the gap on the formal evidence interpretation for the
logic LETj. At the same time, this combination permits a whole
treatment of contradictions, both local and global, including a
gradual handling of the notion of contradiction, thus obtaining a
really useful tool for AI and machine learning, with potential
applications in logic programming via appropriate resolution rules. Popper's Conditional Probability, Negation and Consistency School of Technology Limeira Campus State University of Campinas –UNICAMP Popper' s Conditional Probability, Negation and Consistency
Juliana Bueno-Soler
School of Technology
Limeira Campus
State University of Campinas –UNICAMP
The concept of conditional probability is a formidable tool for
describing the influence of one event on another and plays a
fundamental role in the theory of probability. The usual Kolmogorovian
definition based on a ratio is too restrictive and prone to paradoxes,
even when dealing with probabilities based on non-classical logics. Several axiomatizations of probability theory taking into account the
concept of conditional probability as a primitive notion have been
proposed in an attempt to save the key idea of conditional
probability, K. Popper's proposal being the most successful. This
paper proposes an extension of Popper's account founded on
paraconsistency, by defining a wide notion of conditional probability
based on the Logics of Formal Inconsistency. This leads to an
interesting new theory of paraconsistent conditional probability which
naturally reduces to the standard Popperian axiomatization when events
are taken as consistent, and further reduces to ordinary probability
theory. ## An Epistemic Generalization of RationalizabilityDepartment of Computer and Information Science Brooklyn College CUNY Rationalizability, originally proposed by Bernheim and Pearce, generalizes the notion of Nash equilibrium. Nash equilibrium requires common knowledge of strategies. Rationalizability only requires common knowledge of rationality. However, their original notion assumes that the payoffs are common knowledge. We generalize the original notion of rationalizability to consider situations where agents do not know what world they are in, or where some know but others do not know. Agents who know something about the world can take advantage of their superior knowledge. It may also happen that both Ann and Bob know about the world but Ann does not know that Bob knows. How might they act? We will show how a notion of rationalizability in the context of partial knowledge, represented by a Kripke structure, can be developed. |

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