*Please note that in February and March the LIRa seminar will be held on WEDNESDAYS at 4:30.*

On Wednesday, March 26,** **we will have a joint LogiCIC/LIRa session with** two 35 minutes talks** (with a short break in between) by ** Francesca Poggiolesi **and

**. Everyone is cordially invited!**

**Brian Hill**Speakers: **Francesca Poggiolesi **(CNRS-CEPERC) and **Brian Hill **(CNRS-GREGHEC)

Date and Time: Wednesday, March 26, 2014, **16:30-18:00 **(first talk: 16:30-17:10, second talk: 17:20-18:00)**
**Venue: Science Park 107, Room

**F1.15**

———————————————————————

Speaker: **Francesca Poggiolesi **(CNRS-CEPERC)

Title: **An alternative proof-theoretical approach to standard conditional logics**

Time: 16:30 – 17:10

Abstract:

Conditional logics, which have a long and venerable history [5, 2, 3], have been introduced to capture counterfactual sentences, i.e. conditionals of the form “if A were the case, then B would be the case”, where A is false. If we interpret counterfactuals as material implications, we have that all counterfactuals are trivially true, and this is an unpleasant conclusion. By means of conditional logics, on the other hand, we can give a different and meaningful interpretation of counterfactual sentences.

There are several different systems of conditional logics. Amongst them we focus on the system CK and its standard extensions, namely CK + {ID, MP, CS, CEM}. These systems have a simple and useful semantics. One just needs to consider a set of possible worlds *W*, and a selection function *f*; for each world *i* and each formula *A*, *f* selects the set of worlds of *W* which are *closer* to *i *given the information *A*. Thus a counterfactual sentence *A > B* is true at a world *i* if, and only if, *B* is true at all those worlds that are closer to *i* given the information *A*.

In this talk we aim at presenting sequent calculi for the system CK and all of its extensions. These calculi are based on and fully exploit the simple semantics interpretation of such systems. Moreover, they are contraction-free, weakening-free and cut-free; finally, their logical rules are all invertible. As far as we know the only other sequent calculi that have been proposed for the system CK and its extensions are those of Olivetti and al. [4] (sequent calculi for other systems of conditional logics have been proposed by e.g. [1]). With respect to these calculi the main differences consist in a lighter formalisms and simpler logical rules to manipulate.

By using the same technique adopted for the sequent calculi, we will also briefly show how to construct natural deduction calculi for CK + {ID, MP, CS, CEM}.

References

[1] Crocco, G. and Lamarre, P. On the connection between non-monotonic inference systems and conditional logics. In *Proceedings of the 3rd International Conference on Principles of Knowledge. Representation and Reasoning*, B. Nebel and E. Sandewall Ed., 565-571, 1992.

[2] Lewis, D. *Counterfactuals*. Basil Blackwell, 1973.

[3] Nute, D. *Topics in Conditional Logic*. Reidel, Dordrecht, 1980.

[4] Olivetti, N., Pozzato, G. L., and Schwind, C. B. A sequent calculus and a

theorem prover for standard conditional logics, ACM Transactions on Computational Logic (TOCL) 8 : 557-590, 2007.

[5] Stalnaker, R. A theory of conditionals, American Philosophical Quarterly, Monograph Series no.2, Blackwell, Oxford, 98-112, 1968.

——————————————————————-

Speaker: **Brian Hill **(CNRS-GREGHEC)

Title: **Confidence in Beliefs and Decision Making
**Time: 17:20 – 18:00

Abstract:

The standard representation of beliefs in decision theory and much of formal epistemology, by probability measures, is incapable of representing an agent’s confidence in his beliefs. However, as shall be argued in this talk, the agent’s confidence in his beliefs plays, and should play, a central role in many of the most difficult decisions which we find ourselves faced with. The aim of this talk is to formulate a representation of agents’ doxastic states and a (axiomatically grounded) theory of decision which recognises and incorporates confidence in belief. Time-permitting, consequences for decision in the face of radical uncertainty will be examined.