This Week in Logic at CUNY

 

Computational Logic Seminar
November 20, Time 2:00 – 4:00 PM, Room 3309
Speaker: Evangelia Antonakos, CUNY
Title: Explicit Generic Common Knowledge

Abstract: The name Generic Common Knowledge (GCK) was suggested by
Artemov to capture a state of a multi-agent epistemic system that
yields iterated knowledge I(φ): ‘any agent knows that any agent knows
that any agent knows…φ’ for any number of iterations. In contrast,
generic common knowledge of φ, GCK(φ), yields I(φ),
GCK(φ)→ I(φ)
but is not necessarily logically equivalent to I(φ). Modal logics with
GCK were suggested by McCarthy and Artemov. It has been shown that in
the usual epistemic scenarios, GCK can replace the conventional common
knowledge. Artemov noticed that such epistemic actions as public
announcements of atomic sentences, generally speaking, yield GCK
rather than the conventional common knowledge.
In this talk we introduce logics with explicit GCK and show that they
realize corresponding modal systems, i.e., GCK, along with the
individual knowledge modalities, can be always made explicit. As a
representative example of these explicit GCK systems, we assume that
all knowers as well as their GCK system are confined to LP. We call
the resulting system LPn(LP) which symbolically indicates n LP-type
agents with an LP-type common knowledge evidence system. We then show
this corresponds to the modal GCK system S4nJ by offering a
realization theorem. In particular, all epistemic operators in S4nJ,
not only J, become explicit in such a realization.

NY Philosophical Logic Group
Tuesday, Nov 20, 7:15-9:15 p.m.
2nd floor seminar room, NYU Philosophy Dept (5, Washington Place)
Speaker: Hitoshi Omori, Kobe University, Visiting Fellow, Grad Center, CUNY
Title: Recent developments on systems with the consistency operator

Abstract: Non-classical logics that deny ex contradictione quodlibet
are said to be paraconsistent. Since the monumental work of Jaskowski
in 1948, a large number of paraconsistent systems have been developed.
In this talk, we focus on the consistency operator which is the
characteristic connective of da Costa’s systems. The main motivation
for adding the consistency operator is to make explicit, within the
system, the area in which you can infer classically. The aim of the
talk is threefold. First, we present some results within the framework
of Logics of Formal Inconsistency (LFIs) that generalizes da Costa’s
idea. Second, we show that the consistency operator may be employed,
in a sense to be specified, in developing other paraconsistent logics
such as modal logics, Nelson’s systems and the four-valued logic of
Belnap and Dunn. Finally, we consider two questions related to the
consistency operator. Those are (i) whether the consistency operator
forces us to accept classical negation, and (ii) whether naive set
theories based on LFIs can be developed.

 

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