Quantifier spreading and the question under discussion

Children often display non-adult-like behaviors when reasoning with quantifiers and logical connectives in natural language. A classic example of this is the symmetrical interpretation of universally quantified statements like “Every girl is riding an elephant”, which children often reject as false when they are used to describe a scene with, e.g., three girls each riding an elephant and a fourth elephant without a rider. We present evidence that children’s understanding of these sentences is not attributable to syntactic, semantic, or general processing limitations. Instead, in two experiments, we argue that children’s behavior stems primarily from difficulty in correctly identifying the speaker’s intended “question under discussion”, and that when this question is made contextually unambiguous, children’s judgments are almost completely adultlike.

Unsaid Thoughts: Thinking in the absence of (some) verbal logical connectives

Combining two thoughts into a compound mental representation is a central feature of our verbal and non-verbal logical abilities. We here approach this issue by focusing on the contingency that while natural languages typically verbalise only two of the sixteen connectives from formal logic to express compound thoughts —"and" and "or"— the remainder appear to be entertainable as non-verbal, conceptual representations and this suggests a way to probe how linguistic and non-linguistic thinking processes relate. In a visual world experiment aimed at tracking both comprehension-related and reasoning-related aspects of the capacity to represent compound thoughts, we found that participants are capable of learning and interpreting a made-up word for logic’s NAND operator, indicating that unlexicalised logical connectives are nonetheless conceptually available.

Processing Non-at-Issue Meanings of Conditional Connectives: The wenn/falls Contrast in German

Logical connectives in natural language pose challenges to truth-conditional semantics due to pragmatics and gradience in their meaning. This paper reports on a case study of the conditional connectives (CCs) wenn/falls ‘if/when, if/in case’ in German. Using distributional evidence, I argue that wenn and falls differ in lexical pragmatics: They express different degrees of speaker commitment (i.e., credence) toward the modified antecedent proposition at the non-at-issue dimension. This contrast can be modeled using the speaker commitment scale (Giannakidou and Mari, 2016), i.e., More committed<WENN p, FALLS p>Less committed. Four experiments are reported which tested the wenn/falls contrast, as well as the summary of an additional one from Liu (2019). Experiment 1 tested the naturalness of sentences containing the CCs (wenn or falls) and conditional antecedents with varying degrees of likelihood (very likely/likely/unlikely). The starting prediction was that falls might be degraded in combination with very likely and likely events in comparison to the other conditions, which was not borne out. Experiment 2 used the forced lexical choice paradigm, testing the choice between wenn and falls in the doxastic agent’s conditional thought, depending on their belief or disbelief in the antecedent. The finding was that subjects chose falls significantly more often than wenn in the disbelief-context, and vice versa in the belief-context. Experiment 3 tested the naturalness of sentences with CCs and an additional relative clause conveying the speaker’s belief or disbelief in the antecedent. An interaction was found: While in the belief-context, wenn was rated more natural than falls, the reverse pattern was found in the disbelief-context. While the results are mixed, the combination of the findings in Experiment 2, Experiment 3 and that of Experiment 4a from Liu (2019) that falls led to lower speaker commitment ratings than wenn, provide evidence for the CC scale. Experiment 4b tested the interaction between two speaker commitment scales, namely, one of connectives (including weil ‘because’ and wenn/falls) and the other of adverbs (factive vs. non-factive, Liu, 2012). While factive and non-factive adverbs were rated equally natural for the factive causal connective, non-factive adverbs were preferred over factive ones by both CCs, with no difference between wenn and falls. This is discussed together with the result in Liu (2019), where the wenn/falls difference occurred in the absence of negative polarity items (NPIs), but disappeared in the presence of NPIs. This raises further questions on how different speaker commitment scales interact and why.

Intuiciones en lógica: una propuesta moderada

Intuitions play a significant role in debates about logic. In this paper, I analyze how legitimate is that practice. In the first part of the paper, I distinguish between theoretical and pretheoretical intuitions, and argue that some pretheoretical intuitions are not to be taken into account in logic. Particularly, our pretheoretical intuitions about the concept of validity are not of much importance, since we don’t have a uniform or clear concept of validity in the natural language to be elucidated. Nevertheless, I argue that, since logical connectives are more homogeneously used in our ordinary speech, we can appeal to pretheoretical intuitions to establish their meaning in a logical theory. In the second part of the paper, I consider and reply to four objections to this moderate proposal. Two of them try to show that, if this position is adopted, then the pretheoretical intuitions about the connectives are completely unreliable and useless. One of them argues that this mixed position is unstable: pretheoretical intuitions about the connectives are also pretheoretical intuitions about validity. The last problem is related to the definition of validity and the possibility of revising it.

Truth Tables Without Truth Values: On 4.27 and 4.42 of Wittgenstein’s Tractatus

In 4.27 and 4.42 of his Tractatus Wittgenstein introduces quite complicated formulas, which are equivalent to $$2^n$$ 2 n and $$2^{2^{n}}$$ 2 2 n . This paper shows, however, that the formulas Wittgenstein presents fit particularly well with the way he thinks about truth values, logical connectives, tautologies, and contradictions. Furthermore, it will be shown how Wittgenstein could have avoided truth values even more radically. In this way it is demonstrated that the reference to truth values can indeed be substituted by talking of existing and non-existing facts.

Connecting Sequent Calculi with Lorenzen-Style Dialogue Games

Lorenzen has introduced his dialogical approach to the foundations of logic in the late 1950s to justify intuitionistic logic with respect to first principles about constructive reasoning. In the decades that have passed since, Lorenzen-style dialogue games turned out to be an inspiration for a more pluralistic approach to logical reasoning that covers a wide array of nonclassical logics. In particular, the close connection between (single-sided) sequent calculi and dialogue games is an invitation to look at substructural logics from a dialogical point of view. Focusing on intuitionistic linear logic, we illustrate that intuitions about resource-conscious reasoning are well served by translating sequent calculi into Lorenzen-style dialogue games. We suggest that these dialogue games may be understood as games of information extraction, where a sequent corresponds to the claim that a certain information package can be systematically extracted from a given bundle of such packages of logically structured information. As we will indicate, this opens the field for exploring new logical connectives arising by consideration of further forms of storing and structuring information.

The Perceptual-cognitive Foundation of the Subject-predicate Structure

This article describes a theoretical attempt to found thesubject predicate structure of declarative sentences on a frameworkof the human perceptual cognitive system. The basis of this studyis the idea that perception and cognition of events in the worldwould form mental representations in the system , a kind of modelsof the events that embody pieces of information about the events.This idea suggests that such models have structures that correspondto grammatical structures of the linguistic expressions thatrepresent the events and express the pieces of informationembodied by the models. The model structure s that correspond tothe subject predicate structure and logical connectives have beenconstructed following the way in which the system should functionto form the models of the events. This construction of thestructures entails propositional logic. Application of the structurest o the liar paradox le ads t o a new solution of this paradox .Keywords:

What is the Meaning of Proofs?

The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further and ask about the meaning of a proof as a whole? In this paper we address this question and lay out a framework to distinguish sense and denotation of proofs. Two questions are central here. First of all, if we have two (syntactically) different derivations, does this always lead to a difference, firstly, in sense, and secondly, in denotation? The other question is about the relation between different kinds of proof systems (here: natural deduction vs. sequent calculi) with respect to this distinction. Do the different forms of representing a proof necessarily correspond to a difference in how the inferential steps are given? In our framework it will be possible to identify denotation as well as sense of proofs not only within one proof system but also between different kinds of proof systems. Thus, we give an account to distinguish a mere syntactic divergence from a divergence in meaning and a divergence in meaning from a divergence of proof objects analogous to Frege’s distinction for singular terms and sentences.

Geometric viewpoint on the quantization of a fuzzy logic

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.