# Delta 10 Logic Workshop

Delta workshops aim to bring logicians from Math, Philosophy and Computer Science together. Delta 10 will be held at Nankai University.

Date: 22 Dec, 2018

会议地点：南开大学数学学院第三报告厅

报名方式：请将参会人数，到达及离开时间，住房要求用邮件发至[email protected]

## Speakers

Lu Jiang(Sun Yat-sen University)

Zhe Lin(Sun Yat-sen University)

Yinhe Peng(University of Chinese Academy of Sciences)

Penghui Yao(Nanjing University)

Jinhe Ye(University of Notre Dame)

## Program

Chair:** Liang Yu**

9:00-9:50 **Yinhe Peng: Basis and metrization problems for some classes of spaces**

10:00-11:40 **Penghui Yao: Some Recent Progress on Quantum Information Complexity**

Chair: **Yue Yang**

14:00-14:50 **Zhe Lin: Finite Model Property of n-Transitive Modal Logic**

15:00-15:50 **Lu Jiang: The Ground of Validity for Formal Consequences in Ockham’s Logic**

16:00-16:50 **Jinhe Ye: The Lascar group as a fundamental group**

## Abstracts

**The Ground of Validity for Formal Consequences in Ockham’s Logic**

Lu Jiang(Sun Yat-sen University)

The third treatise of part III of Ockham’s Summa Logicae is titled “De Consequentiis” and contains 46 chapters. This treatise is complex in structure and content as it integrates the discussion of Aristotelian topics and the medieval obligations into the theory on consequences. Traditional subjects from the Topics of Aristotle are combined with medieval logic theories which are not to be found in Aristotelian Organon. It is the purpose of this paper to discuss the interrelationship between these parts, especially between the semantic framework provided by Aristotle’s Topics and its relevance to Ockham’s rules for valid consequences. Earlier research works often regard Ockham’s consequentiae as implications, but as Peter King convincingly argues, it is more accurate to regard them as inferences. Ockham is well aware of the logically significant difference between implications and inferences. Consequences are distinguished into formal and material consequences. The validity of formal consequences is discussed in terms of meta language when he writes that formal consequences hold (tenent) through an “intrinsic middle” or through an “extrinsic middle”. The so called “middle” (medium) is a rule (regula) for valid consequences which can be understood as rule of inference. Ockham formulates these rules in term logic, although his logic contains also propositional calculus as Ernest Moody, Calvin Normore, Wolfgang Lenzen and others show. Inference rules by the intrinsic middle are grounded in the semantic relationship of terms involved in an inferential argument, for example the superior-inferior relationship between terms, but also at the same time the mode of supposition and syncategorematic words of the sense, as made explicit in the rule “from a superior term which supposits in a distributive mode to its corresponding inferior term which supposits in the same way, the consequence is good”. In comparison, the extrinsic middle is a certain general rule (regula generalis) which takes no special regard of particular terms. Rules of this kind concern merely “general conditions of sentences” (generals condiciones propositionum). Examples are the rule that “from an exclusive sentence to a universal sentence, with the subject and predicate exchanging their position, we have a good consequence”, or “from a premise major on necessity and an assertoric premise minor follows a conclusion on necessity”. The validity of these rules is however not immediately obvious. It is therefore the task of this paper to exam extensively and systematically examples of inference of rules given by Ockham in his Summa Logicae and to find out the ground of their validity. It will be shown that Ockham’s rules for consequences are more complicated than their modern counterparts, the proof for their validity involves both term and propositional logic. It is therefore also necessary to show the interrelationship between rules through an intrinsic middle and Ockham’s nominalist version of the Aristotelian ontology and semantic provided by the Topics. By doing this, I shall discuss how Ockham integrates these parts meaningfully into one treatise on consequences.

**Finite Model Property of n-Transitive Modal Logic**

Zhe Lin(Sun Yat-sen University)

**Basis and metrization problems for some classes of spaces**

Yinhe Peng(University of Chinese Academy of Sciences)

The metrization problem for many types of spaces, e.g., compact spaces, is interesting and important. In some sense, to find a metric is the same as to find the basis of all uncountable spaces. A family of uncountable topological spaces is a basis of all uncountable spaces if every uncountable space has a subspace in the family. We will introduce the background and some progress of the basis problem. Connections and applications to other problems will be given.

**Some Recent Progress on Quantum Information Complexity**

Penghui Yao(Nanjing University)

In the past two decades, information complexity received great attention due to its series of successful applications in theoretical computer science, which as well has vastly enriched traditional information theory. A notable example is communication complexity, a core model in theoretical computer science, where a series of successful applications have been discovered thanks to information complexity. In this model, quantum mechanics has presented unconditionally quantitative or even exponential advantages. In this talk, I will survey some of recent results on classical and quantum information complexity and their applications in communication complexity. I will also present some of the major challenges in this field. If time permitted, I will also talk some results about efficient codes for noisy interactive communication.

**The Lascar group as a fundamental group**

Jinhe Ye(University of Notre Dame)

In this talk, we will discuss how the Lascar galois group of a first-order theory, T, can be naturally identified as the fundamental group of the classifying space associated to the category of models, Mod(T). We will then discuss some examples illustrating how tools from algebraic topology can be used to compute the Lascar group of a theory. We will also talk about generalizations to the context of AECs and questions concerning their higher homotopy. This is joint work with Tim Campion and Greg Cousins.

## Organizers

Longyun Ding (NanKai University )

Zhaokuan Hao (Fudan University)

Yanjing Wang(Peking University)

Ruizhi Yang (Fudan University)

Liang Yu (Nanjing University)