A Note on the Interpolation Property in Tense Logic

It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the interpolation property.     

Danto’s Dialectic

Arthur C. Danto’s Analytical Philosophy of History has a Kantian ambition: to state the conditions that make historical knowledge possible and to show “the unhappy destiny” that attends attempts to extend modes of representation beyond these conditions. Even though Danto’s book fails to achieve this ambition, it succeeds in making a number of important—if neglected—suggestions in the course of its attempt. One concerns the significance of the progressive tense for our thinking about human agency. Another concerns the way agency can impact negatively on the possibility of foreknowledge.

‘Now’ and ‘Then’ in Tense Logic

According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now” and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic.     

Overtensing and the effect of regularity

Regularly inflected forms often behave differently in language production than irregular forms. These differences are often used to argue that irregular forms are listed in the lexicon but regular forms are produced by rule. Using an experimental speech production task with adults, it is shown that overtensing errors, where a tensed verb is used in place of an infinitive, predominantly involve irregular forms, but that the differences may be due to phonological confounds, not to regularity per se. Errors involve vowel‐changing irregular forms more than suffixing inflected forms, with at best a small difference between regular ‐ed and irregular ‐en. Frequency effects on overtensing errors require a model in which the past‐tense and base forms of the verb are in competition and in which activation functions are nonlinear, and rule out models with specialized subnetworks for past‐tense forms. Implications for theories of language production are discussed.     

Can word formation be understood or understanded by semantics alone?

Arguments concerning the relative role of semantic and grammatical factors in word formation have proven to be a wedge issue in current debates over the nature of linguistic representation and processing. In the present paper, we re-examine claims by Ramscar [Ramscar, M. (2002). The role of meaning in inflection: Why the past tense does not require a rule. Cognitive Psychology, 45, 45-94.] that it is semantic rather than grammatical factors that influence the choice of regular or irregular past tense forms for English verbs. In Experiment 1, we first replicated Ramscar's (2002) experiment, which showed semantic influences on choice of past tense inflection. A novel verb, splink, was introduced in a semantic context that was reminiscent of an existing regular or irregular rhyme verb: blink or drink. Participants favored the past tense form (splinked or splank) that matched that of the semantically similar verb. In Experiment 2, we introduced novel verbs in a context suggesting that they were grammatically derived from nouns (i.e., denominals). Some current symbolic processing models propose that regular past tense forms should be preferred for such forms. When Ramscar's (2002) original contexts for derivational verbs were re-tested in this condition, we replicated his failure to find a preference for regular past tense forms. However, when the contexts were modified to make the grammatical process more salient, we did find a preference for regular past tense forms, suggesting that the derivational status might have been ambiguous in the original materials. In Experiment 3, we tested whether acceptability ratings for regular or irregular past tense forms of grammatically derived verbs could be explained by semantic distance metrics or by ratings of noun-to-verb derivational status. Ratings of semantic distance and grammatical derivation were orthogonal factors in Experiment 3. Only derivational status predicted acceptability ratings for regular past tense forms. Taken together, the present results suggest that semantic factors do not explain the regularization of irregular verbs in derivational contexts, although semantic factors can affect the choice of past tense forms in certain circumstances.     

Truth Values,Neither-true-nor-false,and Supervaluations

The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9), and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification.     

Regularity and/or consistency in the production of the past participle?

In the present study we have investigated the acquisition of the past participle of Italian verbs of the second (including mostly irregular verbs) and third (including mostly regular verbs) conjugations in school age children, and with simulations with an artificial neural network. We aimed to verify the extent to which children are sensitive to regularity, as opposed to the consistency in the mapping from the infinitive to the past participle. In particular, we predicted that children would learn at some point that verbs of the second conjugation tend to be irregular, and therefore they would be more likely to produce irregularizations for verbs of this class, compared to the verbs of the third conjugation. However, they should also show sensitivity to the phonological mapping consistency within each subclass, learning to produce correct forms on the basis of phonological similarity. In contrast, children should be more likely to produce regular forms for verbs of the third conjugation. Thus, a larger regularity effect would be expected for verbs of the third than of the second conjugation, leading to the prediction of a regularity by conjugation interaction.     

All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■ⁿ⁺¹_F p → ⁿ_F p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete.     

Why do children learn to say "Broke"? A model of learning the past tense without feedback

Learning the English past tense is characterized by a U-shaped learning function for the irregular verbs. Existing cognitive models often rely on a sudden increase in vocabulary, a high token-frequency of regular verbs, and complicated schemes of feedback in order to model this phenomenon. All these assumptions are at odds with empirical data. In this paper a hybrid ACT-R model is presented that shows U-shaped learning without direct feedback, changes in vocabulary, or unrealistically high rates of regular verbs. The model is capable of learning the default rule, even if regular forms are infrequent. It can also help explore the question of why there is a distinction between regular and irregular verbs in the first place, by examining the costs and benefits of both types of verbs.     

Narcissism lost: On translating and being translated1

The authors present a detailed account of the experiences shared in translating and having one’s work translated. Carneiro maintains that, in order to communicate with their readers, writers should relinquish the narcissistic satisfaction they derive from their texts in the original. Beyond this, she feels that, owing to a good understanding between her and her translator, the creativity in her original text persists in the translation. Brakel introduces himself to the IJPA readership and shows how he works when translating the cultural and linguistic nuances and peculiarities of Brazilian Portuguese. He concludes with some thoughts about the affect he experiences from his original work and the work he has translated.