Restriction without Quantification: Embedding and Probability for Indicative Conditionals

Many modern theories of indicative conditionals treat them as restricted epistemic necessity modals. This view, however, faces two problems. First, indicative conditionals do not behave like necessity modals in embedded contexts, e.g., under ‘might’ and ‘probably’: in these contexts, conditionals do not contribute a universal quantification over epistemic possibilities. Second, when we assess the probability of a conditional, we do not assess how likely it is that the consequent is epistemically necessary given the antecedent. I propose a semantics which solves both problems, while still accounting for the data that motivated the necessity modal view. The account is based on the idea that the semantics of conditionals involves only a restriction of the relevant epistemic state, and no quantification over epistemic possibilities. The relevant quantification is contributed by an attitude parameter in the semantics, which is shifted by epistemic modals. If the conditional is asserted, the designated attitude is acceptance, which contributes a universal quantification, producing the effect of a restricted necessity modal.

On Quantifying Literals in Boolean Logic and its Applications to Explainable AI

Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. In this paper, we complement this by introducing and studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification, discuss the interplay between variable/literal and existential/universal quantification, and identify some classes of Boolean formulas and circuits on which quantification can be done efficiently. Literal quantification is more fine-grained than variable quantification as the latter can be defined in terms of the former, leading to a refinement of quantified Boolean logic with literal quantification as its primitive.

Syntactic patterns of πᾶς as a quantifier in New Testament Greek

In linguistic terms, a quantifier is an item that appears with a noun to specify the number or amount of referents indicated by the noun. In English, various kinds of quantification are lexically differentiated—universal quantification (all), distributive quantification (each), and universal-distributive (every). In Greek, however, quantification is conveyed syntactically using primarily one lexical item, namely πᾶς. In this article, we examine the syntactic patterns of πᾶς as a quantifier from a linguistic point of view with attention to the determination of the noun (articular versus anarthrous), the number of the noun (singular versus plural) and the phrasal word order. We also examine the phenomenon of ‘floating’ quantification in which the quantifier moves to a new position in the noun phrase. Finally, we compare the patterns found in New Testament Greek with those of the quantifier כל in the Hebrew Bible in order to determine the extent and type of Semitic interference with respect to quantification in New Testament Greek grammar.Contribution: The syntactic patterns of πᾶς as a quantifier are identified and the semantic import of each pattern is described. The relationship of πᾶς to the quantifier כל in the Hebrew Bible shows evidence of Semitic interference in New Testament Greek grammar.

Generics as default? Comparing the acquisition of universals and generics in Spanish

This paper reports an experiment that investigates interpretive distinctionsbetween two different expressions of generalization in Spanish. In particular, our aimwas to find out when the distinction between generic statements (GS) such as Tigershave stripes and universal quantified statements (UQS) such as All tigers have stripeswas acquired in Spanish-speaking children of two different age groups (4/5-year-oldsand 8/9-year-olds), and then compare these results with adults. The starting point ofthis research was the semantic distinction between GS and UQS in that the formeradmits exceptions, unlike the latter. On the other hand, cognitive psychologists haveobserved a Generic overgeneralization effect (GOG) consisting in allowing for UQSto be felicitous in the face of exceptions, thus proposing that this “error” stems frompeople misinterpreting UQS as GS and from GS being defaults (simpler, more easilylearned and processed) instead of involving quasi-universal quantification, which wasthe learned view from semantics. In the current paper we aimed to test the “Generics asDefault” (GAD) hypothesis by comparing GS and UQS in three different age ranges.Our data show that, overall, participants accept GS more often than they reject UQS.Moreover, we also confirm a hypothesized interaction between age and NP type (GSvs UQS). Further, we present several data points that are not predicted by the GAD,including an observed decline in the accuracy of GS in the older group of children aswell as in adults with respect to younger children, and that children fail at rejectinggenerics that adults reject.

Objectivity and the Politics of Disciplines

This chapter assesses the bearing of bureaucratic cultures on science, then shows how inferential statistics became standard in medicine and psychology as a response to internal disciplinary weakness and external regulatory pressures. The massive effort to introduce quantitative criteria for public decisions in the 1960s and 1970s was not simply an unmediated response to a new political climate. It reflected also the overwhelming success of quantification in the social, behavioral, and medical sciences during the postwar period. This was not a chance confluence of independent lines of cultural and intellectual development, but in some way a single phenomenon. It is no accident that the move toward the almost universal quantification of social and applied disciplines was led by the United States, and succeeded most fully there. The push for rigor in the disciplines derived in part from the same distrust of unarticulated expert knowledge and the same suspicion of arbitrariness and discretion that shaped political culture so profoundly in the same period. Some of this suspicion came from within the disciplines it affected, but in every case it was at least reinforced by vulnerability to the suspicions of outsiders, often expressed in an explicitly political arena.

Categorization via movement: the syntax and semantics of ambos

ABSTRACT In order to explain the syntactic behavior and describe the meaning of the item ambos in Brazilian Portuguese, we propose, assuming the Distributed Morphology framework, (1) that the acategorial root amb- merges, in the syntactic derivation, to a D that moves from inside a full definite DP, and this D categorizes the root; (2) that amb-+D merges back to the DP which D was the head of; (3) that the lower copy of D is erased (or becomes invisible) when the derivation reaches LF; (4) that the meaning of the combination of D and amb- is defined only if the context provides a unique set of two individuals with the properties defined by the plural NP taken by ambos, and introduces a universal quantification over this set.