The Research Seminar in Logic and Language is a forum for all those who have research interests in logic and its many connections with topics in philosophy and the sciences. Seminar talks will sometimes be given by members of TiLPS or other local researchers presenting their results, but more often we will invite guest speakers. Master students and Research Master students may take this research seminar for credit. Please contact Reinhard Muskens for more information. The seminar meets on Thursdays, from 16:30 until 18:00.

4 February: Room DZ8
The Problem of the Safety of the Agenda in Judgment Aggregation
Ulle Endriss, ILLC, University of Amsterdam

Aggregating the judgments of a group of agents regarding a set of interdependent propositions can lead to inconsistent outcomes. This paradox of judgment aggregation has recently sparked a good deal of interest in Legal Theory, Philosophy, Economics, and Computer Science. I will start with a short introduction to judgment aggregation and then formulate a new problem in this context, the problem of the safety of the agenda (SoA). The agenda is the set of propositions on which the agents have to express an opinion, and SoA asks, for a given agenda, whether we can guarantee that judgment aggregation will never produce an inconsistent outcome for any aggregation procedure satisfying a given set of axioms. I will report on a number of characterisation results, establishing necessary and sufficient conditions for SoA to be satisfied for different combinations of the most important axioms proposed in the literature, as well as complexity results for deciding SoA. No domain-specific background knowledge will be required to follow the presentation.

This is joint work with Umberto Grandi and Daniele Porello.

4 March: Room DZ6
A Copy of Several Reverse Mathematics
Sam Sanders, University of Ghent

Reverse Mathematics is a program in foundations of mathematics initiated by Friedman ([1, 2]) and developed extensively by Simpson ([5]). Its aim is to determine which minimal axioms prove theorems of ordinary mathe- matics. Nonstandard methods have played an important role in this program ([3, 6]). We are interested in Reverse Mathematics where equality is replaced by the nonstandard relation ≈, i.e. equality up to infinitesimals. We obtain a `copy' of Reverse Mathematics for WKL0 in a weak system of nonstandard arithmetic. Surprisingly, the same system is also a `copy' of Constructive Re- verse Mathematics. In this talk, we focus on the (considerable) implications of our results for mathematics, physics and philosphy. No specific knowledge of logic or mathematics is required.

References

[1] Harvey Friedman, Some systems of second order arithmetic and their use, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Canad. Math. Congress, Montreal, Que., 1975, pp. 235--242.
[2] Harvey Friedman, Systems of second order arithmetic with restricted induction, I & II (Abstracts), Journal of Symbolic Logic 41 (1976), 557--559.
[3] H. Jerome Keisler, Nonstandard arithmetic and reverse mathematics, Bull. Symbolic Logic 12 (2006), no. 1, 100--125.
[4] H. Jerome Keisler, Nonstandard arithmetic and reverse mathematics, Bull. Symbolic Logic 12 (2006), no. 1, 100--125. MR2209331 (2006m:03092)
[5] Stephen G. Simpson, Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.
[6] Kazuyuki Tanaka, The self-embedding theorem of WKL0 and a non-standard method, Ann. Pure Appl. Logic 84 (1997), no. 1, 41--49.

18 March: Room DZ8
The Evidential View of Reference-rules
Filip Buekens, TiLPS

We present an account of the function of truths like Dog refers to dogs (= (D)) in rational reconstructions of the execution of communicative intentions as involving recognition and uptake by the intended audience of the speaker. On the proposed account, (D) neither reflects a norm nor exercises its function in virtue of capturing a regularity (although (D)de facto registers a regularity among speakers of English). On the Evidential View we defend, (D)'s role in a rational reconstruction is that of evidence, exploited by speakers when forming structured plans for utterances. These plans are composes of beliefs and hierarchically organized communicative intentions that have as the distinctive Gricean feature that their recognition is essential in the specification of their success-conditions. Recognition is a factive attitude, hence a specimen of knowledge, hence sensitive to evidence. Recognition of the semantic intention – the ground-floor intention in a structured set of communicative intentions that govern communicative actions constitutes the basis on which rests successful recognition of further communicative intentions. Dispositionalists and use-theorists correctly register that (D) is a use-regularity among speakers of English but they neglect the fact that (D) is useful to a speaker and be relevant in rational reconstruction of communicative intentions only if speaker and hearer have registered (D) and are able to exploit it, when forming utterance plans, as evidence that will raise the probability of their belief that communicative intentions will be correctly recognized. The authors discusses are Grice, Davidson, Horwich and Hattiangadi.

8 April: Room DZ5
Quantifier Processing
Jakub Szymanik, ILLC, University of Amsterdam

The starting point of our research is a computational model of quantifier processing posited by many linguists and logicians (see van Benthem, 1986). In the model every natural language quantifier is associated with the minimal automata recognizing whether the quantifier sentence is true in a given situation. Various quantifiers demand different computational resources: logical quantifiers ('all', 'some') can be recognized by 2-state finite automata (FA), numerical quantifiers ('at least k') needs a FA with the number of states which allows to count up to k, parity quantifiers ('an even number of') can be processed by 2-state FA with an additional mechanism of parity judgements (loops). Finally, there is no FA recognizing proportional quantifiers ('more than half') as they demand computational mechanism with unbounded memory storage, like push-down automata.
We conducted series of experiments verifying the computational model of simple quantifier comprehension (Szymanik and Zajenkowski, 2009). Our investigations continue previous neuropsychological studies in this area (see McMillan et al., 2005; Troiani et al., 2009). We argue that distinction between first-order and higher-order quantifiers, proposed by the authors of cited papers, do not coincide with the computational resources like working memory, required to compute the meaning of quantifiers. We believe that cognitive difficulty of quantifier processing might be better assessed on the basis of complexity of the minimal corresponding automata (see Szymanik, 2007).
Our first study has shown that time needed for understanding different types of quantifiers is determined by the minimal automata corresponding to the quantifier. We observed that mean reaction time increased as follows: logical quantifiers, parity quantifiers, numerical quantifiers and proportional quantifiers.
Among others, the results indicated that the numerical quantifiers are processed faster than the proportional quantifiers. This observation is consistent with the computational model, i.e., that proportional quantifiers demand a recognition device with qualitatively different internal memory mechanism. We verified this hypothesis empirically. We created situation similar to the span task to assess how subjects are judging the truth-value of statements containing natural language quantifiers with additional memory load. The experiment was a combined task and consisted of two elements. It required participants to verify sentences and to memorize a sequence of single digits for the later recall. The results support hypothesis that working memory resources are involved in processing of the proportional quantifiers to the different degree than in the case of other quantifiers.
Recently, we have been also conducting the same test with schizophrenic patients. The data suggest that the executive aspects of working memory (rather than storage function) are responsible for the processing of proportional quantifiers.
A future research focusing on neurocognitive modeling of quantifier comprehension could help in clarifying the interrelations among computational aspects and their cognitive correlates. The aim would be to pin down the specific cognitive mechanisms responsible for quantifier comprehension, taking into account factors like the role of central executive, attentional costs, storage functions as well as aspects of representing and approximating quantities.

References

1. van Benthem, J. (1986). Essays in logical semantics. Reidel.
2. McMillan, C., et al. (2005). Neural basis for generalized quantifiers comprehension. Neuropsychologia, 43, 1729-1737.
3. Szymanik, J. (2007). A note on a neuroimaging study of natural language quantifiers comprehension, Neuropsychologia, 45, 2158-2160.
4. Szymanik J. and Zajenkowski M. (2009). Comprehension of Simple Quantifiers. Empirical Evaluation of a Computational Model. Cognitive Science: A Multidisciplinary Journal, forthcoming.
5. Troiani, V., et al. (2009). Is it logical to count on quantifiers? Neuropsychologia, 47, 104-111.

22 April: Room DZ5
Between Logic and Common Sense: Word Meaning and Sentence Meaning in Natural Language
Yoad Winter, Utrecht University

People understand language using a complex interplay of logical principles and common sense reasoning. In this talk I will describe on-going work about the effects of common sense reasoning on the meaning of words, and the way it partakes in the logical understanding of full sentences.
After a brief historical overview of logical approaches to natural language semantics, I will give two examples of the interplay between common sense reasoning and such traditional approaches. I will discuss potential relations between prototypicality effects (E. Rosch, E. E. Smith) with words and the logic of reciprocal expressions ("each other", "mutually"). Such relations, if established, may shed new light on broader aspects of semantic processing. Further, I will illustrate the role of common sense reasoning in the analysis of quantificational effects with spatial reasoning in natural language.

6 May: Room DZ5
Modal Interpretations of Temporal Expressions
Stefan Kaufmann, Northwestern/Göttingen

This talk is concerned with the modal implications associated with non-veridical uses of expressions of temporal precedence. One well-known such expression is English "before" on its non-veridical uses, whose modal meaning is often paraphrased with counterfactual conditionals and analyzed in terms of "likely" but unrealized courses of events. On closer inspection, however, it turns out that the relevant notion of "likelihood" is not the same in 'before'-sentences and counterfactuals, and moreover, that neither one corresponds to the intuitive "plain vanilla" likelihood involved in predicting how the world will likely develop past its history up to a given time. The picture is even more interesting in light of cross-linguistic data. I discuss two Japanese expressions in some detail, 'mae' 'before' and '-nai uti' (lit. 'while not yet'), both corresponding to English 'before' in their temporal import, but different in their modal connotations. Following a discussion of the relevant data and intuitive generalizations, I suggest ways in which the subtle differences between the various notions of "likelihood" involved can be teased apart in a formal account.

Note: Some parts of this material are joint work with Cleo Condoravdi and/or Yukinori Takubo.

20 May: Room WZ103
Assertoric Semantics
Stefan Wintein, Tilburg University

Assertoric semantics is an inferential semantics, developed in my PhD thesis, for languages of self-referential truth. The assertoric value of a sentence reports the possibility to live up to the commitments that are associated with the two assertoric acts with respect to that sentence; the acts of asserting and of denying a sentence. As an example, it is neither possible to live up to the commitments one faces if one assert or denies a Liar, while it is possible to live up to both the commitments that one faces by respectively asserting or denying a Truthteller. Assertoric semantics is a four valued semantics, differentiating between the semantic value of the Liar and the Truthteller, and this feature alone distinguishes the approach from most other semantic approaches to self-referential truth. In the literature, semantic accounts of self-referential truth are typically based on a philosophical interpretation of a Kripkean minimal fixed point (e.g. Tim Maudlin, Scott Soames). Minimal fixed points are associated with a three valued semantics, in which Truthtellers and Liars are equated, i.e. they receive the same semantic value, which we may call ungrounded. The rough idea is that a sentence is ungrounded just in case "the world" does not force it to be true or false, which happens to be the case with Liars and Truthtellers. Formally, "the world" is cashed out as a model for the truth free fragment of one’s language and so the standard approach to self-referential truth found in the literature is that of a model-theoretic semantics. In this talk I will compare the model-theoretic account of self-referential truth as given by a Kripkean minimal fixed point with the inferential account as given by assertoric semantics and I will argue that assertoric semantics gives us the better account of self-referential truth.