# Residuals and Conjugates in Positive Substructural Logics

### Andrew Tedder

While the relations between an operation and its residuals play an essential role in substructural logic, a closely related relation between operations is that of conjugation — so closely related that with Boolean negation, the conjugates and residuals of an operation are interdefinable. In this talk extensions of Positive Non-Associative Lambek Calculus including conjugates (and residuals) of fusion are investigated. Some interesting properties of the conjugates are discussed, a proof system is presented, its adequacy questioned, and some further logics with conjugated operations are pondered.

# Temporal reference in non-specific indefinites

### Yael Sharvit

Non-specific indefinite noun phrases in attitude environments can be transparent or opaque. The interpretation of temporal expressions inside the indefinite is constrained by transparency/opacity. The first fact follows from standard assumptions about attitude reports; the second does not. I propose an account that derives both these facts.

# Routley-Meyer relational semantics for some variants of Bradys´s 4-valued matrix

### Sanda María López Velasco

On the one hand, the well-known logic BN4 was defined by R.T. Brady in 1982 and can be considered as the 4-valued logic of the relevant conditional. On the other hand, Routley-Meyer type ternary relational semantics is the semantics introduced by these authors in order to model the logic of relevance. Part of my current research involves applying a R-M semantics to different logics built upon some variants of MBN4 (the matrix of BN4) which verify the Routley and Meyer basic logic B.

The aim of this talk is to display these logics briefly and the reason why they could be of some interest. I will also explain how a R-M semantics can be applied to them.  Considering this, I will provide a general outline of the soundness and completeness theorems, valid for all these logics, and focus on the (corresponding) postulates proofs, which on the contrary need to be specified in each of these logics.

# UConn Logic Group Launches New Certificate Program

The Logic Group is pleased to announce that the Graduate Certificate in Logic is now accredited—which means that we can start awarding it!

A website explaining the certificate in detail is in the works. We hope to have this up by the time the new semester starts.

In the meantime, here is a rough summary:

The participation in the Logic Colloquium needs to be made official by way of taking a one-credit independent study with one of the logic certificate directors (or any other Logic Group faculty member who is willing), with the Logic Colloquium as “course content”.  Please contact any of the three logic certificate directors, Magda, Damir, or Marcus, if you have any questions about any of this or to apply for a having the logic certificate awarded.

• CSE 5102 – Advances Programming Languages
• CSE 5506 – Computational Complexity
• LING 5410 – Semantics I
• LING 5420 – Semantics II
• LING 6410 – Semantics Seminar
• LING 6420 – Topics in Semantics
• MATH 5026 – Topics in Mathematical Logic
• MATH 5260 – Mathematical Logic I
• PHIL 5307 – Logic
• PHIL 5311 – Properties of Formal Systems
• PHIL 5344 – Seminar in Philosophical Logic

# The syntax and semantics of contractual offers

### Joe Buffington

I will be talking about the syntax and semantics of contractual offers. In particular, I will be exploring whether there are any linguistic reasons for modeling contractual offers (as in, “If you do X for me, then I’ll do Y for you.”) as conditional promises, as is often taken to be the case in the legal literature.

# The pragmatics of truth-value judgments

### Gregory Scontras

Investigations of linguistic meaning crucially rely on truth-value judgments: whether a sentence can truthfully describe a given scenario. On the basis of such judgments, researchers have concluded that young children perform quite differently from adults when it comes to understanding ambiguous utterances with multiple potential meanings. For example, when adults hear “Every horse didn’t jump over the fence,” they entertain two interpretations: either none of the horses jumped or not all of the horses jumped. Children usually only endorse the “none” interpretation, rejecting the utterance in a scenario where only two out of three horses jumped. However, subtle changes to the truth-value judgment task setup make children more adult-like. I summarize key results from the literature on child ambiguity resolution, noting three core variables that affect children’s disambiguation behavior. One of these variables concerns children’s processing ability: how easy it is to access the different grammatical interpretations. The other two variables concern children’s ability to manage the pragmatic context: understanding what the topic of conversation is, and modulating expectations about the world being described. I also highlight the nature of the truth-value judgment task children are being asked to engage in, which I then formally articulate using a cognitive computational model that specifies the role of each of these three variables in providing truth-value judgments. The results suggest that pragmatic factors play a larger role than processing factors in explaining children’s non-adult-like ambiguity resolution behavior, and the computational modeling framework allows us to understand exactly why that’s so. Indeed, by modeling the task itself, we see that the truth-value judgment data typically used to demonstrate children’s difficulty with ambiguity in fact require no disambiguation at all — just the ability to manage the pragmatics of the task.

# Character assassination: de se semantics for indexicals

### Craige Roberts

Claim: Both the directly referential semantics and the more recent anaphoric accounts of 1st and 2nd person indexicals offer a picture of indexicality which is empirically and conceptually inadequate. They fail to capture this fact: Indexicals are essentially perspectival, as reflected in the fact that 1st and 2nd person indexicals are always de se.

Why hasn’t that been evident before?

Here is something important that compositional semantics has taught us: You cannot properly assess the meaning of an expression without considering its use and meaning in embedded contexts. But, as Kaplan drove home, the English 1st and 2nd person pronouns never seem to vary in interpretation in embedded contexts. However, recent work in linguistics has uncovered a wide variety of unrelated languages where the 1st and 2nd person pronouns can be shifted under attitudes. Careful consideration of their shifted meanings offers a new perspective on indexicality. Accordingly, I offer arguments for a de se account of indexicality.

# Ultraproducts and saturation

### Reed Solomon

This talk will be an introduction to the ultraproduct construction and the model theoretic notion of saturation, which are two of the themes in Maryanthe Malliaris’s Annual Logic Lecture next week. My goal is to introduce these concepts with some examples and motivation to give anyone interested some familiarity with the key characters in Maryanthe’s story before she arrives. Maryanthe will define these concepts in her talk and will not presuppose any material from my talk.

# The Strict-Tolerant Interpretation of the Weak Kleene Matrices

### Thomas Ferguson

The framework of strict-tolerant consequence championed by Cobreros, Egré, Ripley and van Rooij provides a novel setting that permits one to have a transparent truth predicate without abandoning classical logic. The semantics for this notion of consequence, due to van Rooij, employs the three-valued strong Kleene matrices. A second framework that has received renewed attention is the collection of weak Kleene matrices, which have frequently appeared in the context of so-called logics of nonsense, making the pairing of these topics a natural avenue for investigation. In this talk, I’ll discuss strict-tolerant consequence on the weak Kleene matrices, its corresponding proof theory, and its interpretation. I’ll also discuss how the resulting notion of consequence bears on several matters in philosophical logic, including the content-theoretic interpretation of bounds consequence, the semantic properties of paradoxical sentences in the Principia Mathematica, and debates concerning the logical analysis of category mistakes.