Quantum Structure in Cognition, Origins, Developments, Successes and Expectations

We provide an overview of the results we have attained in the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. We firstly discuss the quantum foundational reasons that led us to investigate the mechanisms of formation and combination of concepts in human reasoning, starting from the empirically observed deviations from classical logical and probabilistic structures. We then develop our quantum-theoretic perspective in Fock space which allows successful modeling of various sets of cognitive experiments collected by different scientists, including ourselves. In addition, we formulate a unified explanatory hypothesis for the presence of quantum structures in cognitive processes, and discuss our recent discovery of further quantum aspects in concept combinations, namely, 'entanglement' and 'indistinguishability'. We finally illustrate perspectives for future research.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1412.870

The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictory Powers in the Potential Realm

In [7] the authors of this paper argued in favor of the possibility to consider a Paraconsistent Approach to Quantum Superpositions (PAQS). We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints -coming from present technical and experimental developments in QM- that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against the PAQS [1, 2, 3]. In [11, 12] it was argued that their reasoning presupposes a metaphysical stance according to which the physical representation of reality must be exclusively considered in terms of the equation: Actuality = Reality. However, from a different metaphysical standpoint their problems disappear. It was also argued that, if we accept the idea that quantum superpositions exist in a (contradictory) potential realm, it makes perfect sense to develop QM in terms of a paraconsistent approach and claim that quantum superpositions are contradictory, contextual existents. Following these ideas, and taking as a standpoint an interpretation in terms of the physical notions of power and potentia put forward in [10, 12, 15], we present a paraconsistent formalization of quantum superpositions that attempts to capture the main features of QM.Comment: 26 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1502.05081, arXiv:1404.5186, arXiv:1506.0737

Negation 'presupposition' and metarepresentation: a response to Noel Burton-Roberts

Metalinguistic negation (MN) is interesting for at least the following two reasons: (a) it is one instance of the much broader, very widespread and various phenomenon of metarepresentational use in linguistic communication, whose semantic and pragmatic properties are currently being extensively explored by both linguists and philosophers of language; (b) it plays a central role in recent accounts of presupposition-denial cases, such as ‘The king of France is not bald; there is no king of France’. It is this latter employment that discussion of metalinguistic negation has focused on since Horn (1985)'s key article on the subject. While Burton-Roberts (1989a, 1989b) saw the MN account of presupposition-denials as providing strong support for his semantic theory of presupposition, I have offered a multi-layered pragmatic account of these cases, which also involves MN, but maintains the view that the phenomenon of presupposition is pragmatic (Carston 1994, 1996, 1998a)

Not wacky vs. definitely wacky: A study of scalar adverbs in pretrained language models

Vector space models of word meaning all share the assumption that words occurring in similar contexts have similar meanings. In such models, words that are similar in their topical associations but differ in their logical force tend to emerge as semantically close, creating well-known challenges for NLP applications that involve logical reasoning. Modern pretrained language models, such as BERT, RoBERTa and GPT-3 hold the promise of performing better on logical tasks than classic static word embeddings. However, reports are mixed about their success. In the current paper, we advance this discussion through a systematic study of scalar adverbs, an under-explored class of words with strong logical force. Using three different tasks, involving both naturalistic social media data and constructed examples, we investigate the extent to which BERT, RoBERTa, GPT-2 and GPT-3 exhibit general, human-like, knowledge of these common words. We ask: 1) Do the models distinguish amongst the three semantic categories of MODALITY, FREQUENCY and DEGREE? 2) Do they have implicit representations of full scales from maximally negative to maximally positive? 3) How do word frequency and contextual factors impact model performance? We find that despite capturing some aspects of logical meaning, the models fall far short of human performance.Comment: Published in BlackBoxNLP workshop, EMNLP 202

The critics of paraconsistency and of many-valuedness and the geometry of oppositions

In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics

Vagueness, Logic and Use: Four Experimental Studies on Vagueness

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negatio

The New Quantum Logic

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.Comment: Minor changes and corrections to bring into conformity with published versio