Invited Speakers - Trends in Logic XI

Invited speakers

Giovanna Corsi (University of Bologna, Italy) [...]   

Quantified epistemic systems based on free logic

We investigate various quantified epistemic systems based on free logic and formalized in a language with indexed modalities. Transition semantics will be generalized so as to allow models with inner and outer domains. Well known modal formulas will be discussed in this context. (Joint work with Eugenio Orlandelli.)


Hans van Ditmarsch (University of Sevilla, Spain) [...]

Awareness bisimulation, knowledge, and awareness

We consider semantic structures and logics that differentiate between being uncertain about a proposition, being unaware of a proposition, becoming aware of a proposition, and getting to know the truth value of a proposition. We propose a unified setting to model this variety of static and dynamic aspects of awareness and knowledge. Various derived notions will be discussed: explicit knowledge, implicit knowledge, and also novel epistemic notions such as speculative knowledge (back to the motivation in Levesque's 'A Logic of Implicit and Explicit Belief', one can speculate over variables of which one is unaware, e.g. if you are unaware of p, then p v ~p is still speculatively known by you). A cornerstone of this framework is the notion of awareness bisimulation - this is the proper notion of structural similarity on the structures enriched with awareness of propositional variables proposed by Fagin and Halpern in 'Belief, awareness, and limited reasoning'. Just as bisimilarity preserves logical truth, awareness bisimilarity preserves the truth of which you are aware.
(Joint work with Tim French and Fernando Velazquez.)


Norihiro Kamide (Waseda Institute,Tokyo, Japan) [...]

An embedding-based method for non-classical logics

An embedding-based proof method for some non-classical logics is presented. This method can uniformly prove the cut-elimination, completeness, decidability and Craig interpolation theorems for some non-classical logics including some paraconsistent and temporal logics. This method is based on two theorems for syntactically and semantically embedding the objective non-classical logic into its negation-less or time-less fragment. Firstly in this talk, some results on Nelson's paraconsistent logic and its neighbors, which have recently been obtained by Kamide and Wansing, are presented. Secondly, some results on linear-time temporal logic and its neighbors are presented.


Marcus Kracht (University of Bielefeld, Germany) [...]

Are Logical Languages Compositional?
In this presentation I argue that in contrast to natural languages, logical languages typically are not compositional. This does not mean that the meaning of expressions cannot be determined. It only means that the meaning of an expression cannot be determined without looking at its form. If one is serious about the compositionality of a logic, the only possibility is to define it via abstraction from a variable free language.


Sergei P. Odintsov (Sobolev Institute of Mathematics, Novosibirsk, Russia) [...]

Remarks on Algorithmic Properties of Inconsistency Adaptive Logics

Adaptive logic is a well-developed approach to non-monotonic logic which can be considered as unifying for formalization of default reasoning. Being non-monotonic, such logics usually have rather complex consequence relations. In this presentation, the propositional inconsistency adaptive logics based on strategies of reliability and of minimal abnormality are considered. We present the exact estimations of the algorithmic complexity of adaptive consequence relations for both strategies relativized to the complexity of the premiss set, which generalizes the results obtained earlier by L. Horsten, P. Welch, and P. Verdee. We consider also the possibility of generalization of the obtained results to arbitrary adaptive logics in standard format. (Joint work with Stanislav O. Speranski.)


Rohit Parikh (City University of New York, USA) [...]

Epistemic Logic and Applications to Games

Epistemic Logic entered game theory with the publication in 1976 of Aumann's paper "Agreeing to Disagree" where he showed that under certain conditions two agents could not have common knowledge of the fact that they had different views of some event. This result was extended by a number of authors including ourselves. We will give a brief overview of the results.
Another topic about which we will speak is some recent work, joint with Cagil Tasdemir and Andreas Witzel where we investigate how an agent who furnishes information to some people playing a game can affect the  course of the game by  (selectively) revealing or withholding  some facts about the current status of the game.
Finally we will briefly describe some joint work with Walter Dean on how a candidate running for election will inform the voters about her political views, again, revealing some and withholding some others.


Graham Priest (University of Melbourne, Australia/City University of New York, USA) [...][...]

Indefinite Extensibility – Dialetheic Style

In recent years, many people writing on the paradoxes of self-reference, and especially the set theoretic paradoxes, have invoked the notion of an indefinitely extensible concept. They have all assumed that such concepts must be consistent. The very opposite naturally appears to be the case. There are indeed, indefinitely extensible totalities, but contradictions appear  at the very limits of extensibility.  Of course, to handle dialetheism of this kind requires paraconsistent logic.  This talk will explore how the notion of indefinite extensibility appears from such a perspective.


Gerhard Schurz (Heinrich-Heine University of Düsseldorf, Germany) [...]

Reward versus Risk in Uncertain Inference: Theorems and Simulations

Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper I present an investigation of  four prominent LP systems, the systems O, P, Z, and QC (based on joint work with Paul Thorn). These systems differ in the number of inferences they licence (O is a subset of P is a subset of Z is a subset of QC). LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper I present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper I investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. (Joint work with Paul Thorn.)


Yaroslav Shramko (Pedagogical State University Kryvyi Rih) [...]

Two-faced Truth: Generalized Classical Truth-Values

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemological aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values where each value contains both ontological and epistemological components. This allows one to de ne two unary twin connectives that can be called \semi-classical negations". Each of these negations deals only with one of the above mentioned components, and they may be of use for a logical reconstruction of an argumentative reasoning. We formulate separate consequence systems for the semi-classical negations, and then bring them together within a super-classical logic. (Joint work with Dmitry Zaitsev.)


Ryszard Wójcicki (Polish Academy of Sciences, Warsaw) [...]

Definition vs. Criteria of Truth

Tarski’s warning that no available in the set by him way definition of truth provides criteria of truth is question begging. I argue that without reflecting on that warning one cannot account properly for the idea of truth, its correspondence version included.  

Alberto Zanardo (University of Padova, Italy) [...]

Recognized possibilities (and choices) as moments in branching-time

In branching-time structures, the set of histories passing through a given moment can be partitioned according to suitable equivalence relations. For instance, the tree-like structure of time provides the undividedness relation between histories, while Belnap’s choices correspond to additional requirements on the structure of Time.

In the talk, I will consider the notion of ‘indistinguishability’ as a generalization of the notion of choice. We assume that, at each moment in time (for a given agent a) some histories are indistinguishable from others. Equivalence classes modulo indistinguishability are called recognized possibilities (r.p.), of the agent a, at the moment under consideration. Truth in these structures, for a suitable temporal language, is relative to pairs <moment, r.p.>, while a modal operator quantifies over the set of r.p.’s. When indistinguishability is a choice relation, this provides an interesting perspective under which notions related to agency (and in particular Belnap’s stit) can be considered.

The set of pairs <m., r.p.> can be endowed in a natural way with a tree-like structure, which has significant relations with the starting tree. For instance, if indistinguishability is a choice relation, there is a one-to-one correspondence between the set of histories in the two trees. Moreover, for particular indistinguishability relations, recognized possibilities themselves can be viewed as moments in a branching-time structure. Thus, a natural problem in this context is how logical properties transfer from a tree to the one consisting of r.p.’s.