**3-4 May 2016 Aula Enzo Paci, Department of Philosophy, ****University of Milan**

The purpose of this workshop is to foster cross disciplinary research into applied logics, and in particular logics applied to capturing interesting aspects of practical reasoning. To this end we have asked our speakers to provide accessible presentations of their material and the schedule allows plenty of time for discussion.

Attendance is free, but registration is mandatory.

**Travel Grants**

A limited number of small travel grants are available for PhD student and PostDocs who have no access to funding. Please write to hykel.hosni AT unimi.it to apply.

**Schedule for Tuesday 3 May**

- 14:00 – 14:30 | Arrival and Opening
- 14:30 – 15:30 | Walter Carnielli
- 15:30 – 16:30 | Dov Gabbay

**Schedule for Wednesday 4 May**

- 10:30 – 11:30 | Marcello D’Agostino
- 11:30 – 12:30 | Jeff Paris

**Titles and Abstracts**

*Walter Carnielli: “Probability, Consistency and Evidence”*

I intend to discuss the first steps towards a unifying theory of probability based on logic, regarding probability as a branch of logic in a generalized way. According to this program, one can define in a same set of meta-axioms probability measures that are either classical, paraconsistent, intuitionistic and simultaneously intuitionistic and paraconsistent just by parameterizing on logic systems. In particular, I discuss theories of probability built upon the paraconsistent Logic of Formal Inconsistency Ci, and upon the paraconsistent and paracomplete Logic of Evidence and Truth LETj, a Logic of Formal Inconsistency (LFI) and Undeterminateness (LFU). I argue that LFIs very naturally encode an extension of the notion of probability able to express probabilistic reasoning under excess of information (contradictions), while LFUs encode extensions of the notion of probability able to express probabilistic reasoning under lack of information (incompleteness), and thus better connected to evidence than to truth. LETj is designed to express the notions of conclusive and non-conclusive evidence, as well as preservation of evidence; it is also able to recover classical logic for propositions whose truth-value have been conclusively established. In this way, it can in particular also express the notion of preservation of truth. By means of defining appropriate versions of conditional probability, notions of potential evidence versus veridical evidence can be defined, in contrast to the proposals by Peter Achinstein (The Book of

Evidence, 2001).

*Marcello D’Agostino: An introduction to Depth-bounded Logics*

Logic is informationally trivial and, yet, computationally hard. This is one of the most baffling paradoxes arising from the traditional account of logical consequence. Triviality stems from the widely accepted characterization of deductive inference as non-ampliative: the information carried by the conclusion is (in some sense) contained in the information carried by the premises. Computational hardness stems from the well-known results showing that most interesting logics are undecidable or, even when decidable, very likely to be intractable. This situation leads to the so-called “scandal of deduction” and to the related “problem of logical omniscience”. To address this problem, we present a unifying semantic and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic. These approximations provide a hierarchy of tractable logical systems that indefinitely converge to classical propositional logic and can be usefully employed to model the inferential activity of real-world, resource-bounded agents.

*Dov Gabbay: Talmudic Norms Approach to the Paradox of the Heap: A Position Paper*

This paper offers a Talmudic norms solution to the paradox of the heap. The claim is that the paradox arises because philosophers use the wrong language to discuss it and the appropriate language is that of an extended blocks world language, together with the Talmudic normative theory of mixing (Talmudic calculus of Sorites) and the principle that a property of any mixture (or indeed any object) is also how it was constructed. We seek a correlation between Talmudic positions on mixtures and philosophical positions on Sorites. The Talmud is very practical and cannot allow for any theoretically unresolved paradox to get in the way, and so it has a lot to offer to philosophy.

*Jeff Paris: A Model of Belief, and Truth*

The ENT model of belief was introduced by Alena Vencovska and myself in a paper in AI in 1993 as a way for an agent to form beliefs from direct experience while avoiding the feasibility problems which dogged the alternative probability constraints approaches which were in vogue at that time. Since then two other papers have appeared which provide some further possible support for this ENT model. In my talk I shall sketch the original construction and these subsequent observations.

**Travel Grants**

A limited number of small travel grants are available for PhD student and PostDocs who have no access to funding. Please write to hykel.hosni AT unimi.it to apply.

**Location**

The workshop will take place in “Aula Enzo Paci” at the Direction of the Department of Philosophy, which is located in the University Main Building in Via Festa del Perdono 7.