The paper argues that natural language quantification, as expressed by determiner phrases, is not polysemous. The foil for this claim is Hofweber, who contends that natural language quantification is polysemous between a domain reading and an inferential reading. The thesis is intended to support a more general division between externalist and internalist positions in semantics. The paper, to the contrary, argues that there is no linguistic evidence for polysemous quantification, and Hofweber’s proposal proves (...) to be non-compositional. Further, an approach at least consistent with internalism is available independent of an inferential reading, for natural language quantification can be read as ontologically neutral, which removes the rationale for the polysemy hypothesis. The paper remains neutral on so-called heavyweight vs. lightweight construals of quantification, which are not claims about natural language semantics. (shrink)

This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to the (...) nominal and verbal predicates, where an alternative to a property ψ is one that shares a pragmatic presupposition with ψ, and a pragmatic presupposition is one that is selected by context from a set of potential presuppositions associated with the sentence. A many/few-quantified sentence is then true iff the proportion of the scope to the restrictor is greater/less than some threshold, n. In addition to explaining various problematic cases from the literature, the analysis shows how the readings of a many/few-quantified sentence can be derived from the same syntactico-semantic structure, it being unnecessary to claim lexical or structural ambiguity. The analysis also provides strong support for the idea that natural language quantification is always purely extensional. (shrink)

Cognitive Science, Volume 46, Issue 2, February 2022.

This extended collection of papers is the result of putting recent ideas on quantification to work on a wide variety of languages.

The present paper is an attempt at the investigation of the nature of polarity contrast in natural languages. Truth conditions for natural language sentences are incomplete unless they include a proper definition of the conditions under which they are false. It is argued that the tertium non datur principle of classical bivalent logical systems is empirically invalid for natural languages: falsity cannot be equated with non-truth. Lacking a direct intuition about the conditions under which a sentence (...) is false, we need an independent foundation of the concept of falsity. The solution I offer is a definition of falsity in terms of the truth of a syntactic negation of the sentence. A definition of syntactic negation is proposed for English. (shrink)

The semantic rules governing natural language quantifiers (e.g. "all," "some," "most") neither coincide with nor resemble the semantic rules governing the analogues of those expressions that occur in the artificial languages used by semanticists. Some semanticists, e.g. Peter Strawson, have put forth data-consistent hypotheses as to the identities of the semantic rules governing some natural-language quantifiers. But, despite their obvious merits, those hypotheses have been universally rejected. In this paper, it is shown that those hypotheses are (...) indeed correct. Moreover, data-consistent hypotheses are put forth as to the identities of the semantic rules governing the words "most" and "many," the semantic rules governing which semanticists have thus far been unable to identify. The points made in this paper are anticipated in a paper, published in the same issue of the Journal of Pragmatics, by Andrzej Boguslawski. (shrink)

This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of (...) continuations automatically accounts for scope displacement and scope ambiguity. To prove this claim, I exhibit a simple finite context-free grammar with a strictly compositional semantics in which quantificational NPs are interpreted in situ but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or similar mechanisms used in many recent HPSG, Categorial, or Type-logical treatments), and no need for type-shifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either type-shifting or type polymorphism. Compositionality issues are discussed in some detail. (shrink)

The fifth chapter provides a detailed discussion of Buridan’s strategy of identifying the conceptual structures discussed in the chapter 4 by means of the various “syntactical clues” provided by spoken and written natural languages. The chapter compares the Buridanian strategy of “regimentation” with the modern strategy of formalization, and argues that for the purposes of a “natural logic” the former is not inferior to the latter. But in order to bridge the conceptual gap between the two approaches, the (...) chapter also discusses a simple extension of standard quantification theory that is capable of faithfully representing a large part of Buridan’s logic. Indeed, the chapter argues that the resulting formal system is in accord not only with Buridan’s logic, but with our natural language intuitions in general, providing more faithful representation of natural language reasoning than standard quantification theory. (shrink)

The Realist that investigates questions of ontology by appeal to the quantificational structure of language assumes that the semantics for the privileged language of ontology is externalist. I argue that such a language cannot be (some variant of) a natural language, as some Realists propose. The flexibility exhibited by natural language expressions noted by Chomsky and others cannot obviously be characterized by the rigid models available to the externalist. If natural languages are (...) hostile to externalist treatments, then the meanings of natural language expressions serve as poor guides for ontological investigation, insofar as their meanings will fail to determine the referents of their constituents. This undermines the Realist’s use of natural languages to settle disputes in metaphysics. (shrink)

A volume of studies in natural language semantics which brings together work by philosophers, logicians and linguists. The main topics treated are: quantification and reference in natural language; the relations between formal logic, programming languages and natural language; pragmatics and discourse meaning; surface syntax and logical meaning. The volume derives from a colloquium organised in 1973 by the Kings College Research Centre, Cambridge and the papers have been edited for publication by Professor Keenan. (...) It is hoped that the collection will make available some of the best work in this fast-moving field and will stimulate further progress by juxtaposing the different approaches and interests represented here. (shrink)

This paper has two parts. In part I, I review two older accounts of the logical forms of modifiers, and suggest that they may be combined with each other so as to yield a theory that is better than either of its parts taken singly. Part of this theory involves the idea that certain sentences refer to events, states, or processes; Part II of this paper shows how to use this idea to account for tenses and temporal adverbials, and offers (...) a new account of ordinary language quantification. (shrink)

This work presents the structure, distribution and semantic interpretation of quantificational expressions in languages from diverse language families and typological profiles. The current volume pays special attention to underrepresented languages of different status and endangerment level. Languages covered include American and Russian Sign Languages, and sixteen spoken languages from Africa, Australia, Papua, the Americas, and different parts of Asia. The articles respond to a questionnaire the editors constructed to enable detailed crosslinguistic comparison of numerous features. They offer comparable information (...) on semantic classes of quantifiers (generalized existential, generalized universal, proportional, partitive), syntactically complex quantifiers (intensive modification, Boolean compounds, exception phrases, et cetera), and several more specific issues such as quantifier scope ambiguities, floating quantifiers, and binary (type 2) quantifiers. The book is intended for semanticists, logicians interested in quantification in natural language, and general linguists as articles are meant to be descriptive and theory independent. The book continues and expands the coverage of the Handbook of Quantifiers in Natural Language (2012) by the same editors, and extends the earlier work in Matthewson (2008), Gil and others (2013) and Bach et al (1995). (shrink)

This paper has two parts. In part I, I review two older accounts of the logical forms of modifiers, and suggest that they may be combined with each other so as to yield a theory that is better than either of its parts taken singly. Part of this theory involves the idea that certain sentences refer to events, states, or processes; Part II of this paper shows how to use this idea to account for tenses and temporal adverbials, and offers (...) a new account of ordinary language quantification. (shrink)

. A new approach to the formalization of concepts used in legal reasoning such as obligation and cause is presented. The formalization is based on the linguistic use of the concepts both in legal language and in ordinary language, and has been motivated by work on a legal expert system with a natural language interface. Particularly for the concept of obligation this yields quite different results from those obtained by the usual approach of deontic logic: So‐called (...) paradoxes are avoided, quantification over obligations becomes possible, no restriction to a “single‐agent system” is required, and collisions of obligations can be formulated. (shrink)

Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised quantifiersGeneralised quantifiers for natural language. That technique requires one to construct the vector space over powersets, and therefore is computationally costly. In this paper, we overcome this problem by considering fuzzy versions of quantifiers along the lines of ZadehZadeh, L. A., within the category of many valued relationsMany valued relations. We show that this category is a concrete instantiation (...) of the compositional distributional model. We show that the semantics obtained in this model is equivalent to the semantics of the fuzzy quantifiers of ZadehZadeh, L. A.. As a result, we are now able to treat fuzzy quantification without requiring a powerset construction. (shrink)

In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in (...) polynomial time. Additionally, we suggest that plausible semantic theories of the everyday fragment of natural language can be formulated in the existential fragment of second-order logic. -/- In Chapter 2 we give an overview of the basic notions of generalized quantifier theory, computability theory, and descriptive complexity theory. -/- In Chapter 3 we prove that PTIME quantifiers are closed under iteration, cumulation and resumption. Next, we discuss the NP-completeness of branching quantifiers. Finally, we show that some Ramsey quantifiers define NP-complete classes of finite models while others stay in PTIME. We also give a sufficient condition for a Ramsey quantifier to be computable in polynomial time. -/- In Chapter 4 we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents. We show a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. Additionally, we argue that this difference should be acknowledged in the Strong Meaning hypothesis. -/- In Chapter 5 we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. The type-shifting approach cannot lead outside second-order logic and arguably some collective quantifiers are not expressible in second-order logic. As a result, we argue that algebraic (many-sorted) formalisms dealing with collectivity are more plausible than the type-shifting approach. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics. -/- In Chapter 6 we study the statement known as Hintikka's thesis: that the semantics of sentences like ``Most boys and most girls hate each other'' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading. -/- In Chapter 7 we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model. -/- In Chapter 8 we discuss some general open questions and possible directions for future research, e.g., using different measures of complexity, involving game-theory and so on. -/- In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science. (shrink)

Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars; they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple type theory while committing us to nothing more than the austere ontology (...) of First-Order Logic. Were this true, Higher-Level Plural Logic would be a useful tool, with various applications in philosophy and linguistics. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with a lot of scepticism. In this paper, I argue for the legitimacy of Higher-Level Plural Logic by providing evidence to the effect that natural languages contain higher-level plural expressions and showing that it is likely that they do so in an indispensable manner. Since the arguments I put forward are of the same sort advocates of Plural Logic have employed to defend their position, I conclude that the commonly held view that Plural Logic is legitimate, but not so its higher-level plural extensions is untenable. (shrink)

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further (...) identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle. (shrink)

This paper gives an overview of the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this usual general framework represents a departure from empirical linguistic data. We briefly sketch a different idea for proof theory which is closer to the language itself than standard approaches in many aspects. We stress the importance of Hilbert’s operators—the epsilon-operator for existential and tau-operator for universal quantifications. Indeed, these operators are (...) helpful in the construction of a semantic representation which is close to natural language in particular with quantified noun phrases as individual terms. We also define guidelines for the design of proof rules corresponding to generalized quantifiers. (shrink)

This paper gives an overview of the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this usual general framework represents a departure from empirical linguistic data. We briefly sketch a different idea for proof theory which is closer to the language itself than standard approaches in many aspects. We stress the importance of Hilbert’s operators—the epsilon-operator for existential and tau-operator for universal quantifications. Indeed, these operators are (...) helpful in the construction of a semantic representation which is close to natural language in particular with quantified noun phrases as individual terms. We also define guidelines for the design of proof rules corresponding to generalized quantifiers. (shrink)

We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational (...) complexity results to investigate semantic distinctions between quantified reciprocal sentences. We show a computational dichotomy<br>between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to<br>revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of the formal<br>semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science. (shrink)

This book contains papers from a colloquium held in 1973 at Kings College, Cambridge. The contributions deal with the number of questions on which a great deal of current linguistic research and writing focus. These include the problem of quantification and reference in natural language; the application of formal logic to natural language semantics; the semantics of non-declarative sentences; the relation between natural language semantics and programming languages; the relation between sentences and their (...) contexts of use; discourse meaning; and the relation between surface syntax and logical meaning. An adequate treatment of these issues requires the interaction of a number of different linguistic approaches. As one of the contributors to the volume points out, there recently have developed three major new developments in areas of research into linguistic phenomena: transformational grammar, formal logic, and speech act theory. Although no one of these are represented singly in this volume, a number of the problems which are discussed involve issues which depend on the interfaces between these various approaches. (shrink)

The authors explore Carnap’s (1931) famous critique of Heidegger’s metaphysics and argue that, from the perspective of contemporary formal semantics of natural language, Carnap’s criticism is not convincing. Moreover, they provide direct empirical objections to Carnap’s criticism. In particular, using empirical evidence from languages like Russian that have negative concord, they show that Heidegger cannot be accused of assigning illegitimate logical forms to his sentences about Nothing because terms like “Nothing” can be used non-quantificationally and the fact that (...) it is not clear how their reference is established cannot be the reason why the corresponding sentences are ungrammatical (as Carnap seemed to suggest). The authors also critically discuss the view that natural language is insensitive to meaninglessness or contradiction. With reference to the work of J. Gajewsky, they show that this view is not true either. As a result of this investigation, they arrive at a position that an appeal to ungrammaticality like the one proposed by Carnap does not provide legitimate evidence against metaphysics. This conclusion relates to some recent criticism of the so-called non-analytical philosophers that can be traced back to Carnap’s paper. (shrink)

The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same (...) time, those intentional objects do not come for free; rather they are strictly dependent on intentional acts that generally need to have a presence, in one way or another, in the semantic structure of the sentence. (shrink)

Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

The standard analysis of quantification says that determiner quantifiers (such as every) take an NP predicate and create a generalized quantifier. The goal of this paper is to subject these beliefs to crosslinguistic scrutiny. I begin by showing that in St'á'imcets (Lillooet Salish), quantifiers always require sisters of argumental type, and the creation of a generalized quantifier from an NP predicate always proceeds in two steps rather than one. I then explicitly adopt the strong null hypothesis that the denotations (...) of quantifiers should be crosslinguistically uniform. Since the Salish data cannot be captured by the usual analysis of English, I pursue the idea that English is reducible to the Salish pattern. Reanalysis of many English constructions is required. I argue that the reanalysis has advantages over the standard analysis for partitives, as well as for non-partitive all- and most-phrases, which I analyze as containing bare plurals of argumental type. Even where the new analysis faces some challenges (for example, with every), the attempt still leads to fruitful results. It forces us to view familiar constructions in a new light, and to redefine, I believe correctly, which quantificational constructions are ‘basic’ and which stand in need of further explanation. (shrink)

Some natural language expressions –namely, determiners like every, some, most, etc.— introduce quantification over individuals (or, in other words, they express relations between sets of individuals). For example, the truth conditions of a sentence like (1a) are represented in Predicate Logic (PrL) by binding the..

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in (...) light of structurally diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. (...) Utilizing recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (shrink)

The currently standard philosophical conception of existence makes a connection between three things: certain ways of talking about existence and being in natural language; certain natural language idioms of quantification; and the formal representation of these in logical languages. Thus a claim like ‘Prime numbers exist’ is treated as equivalent to ‘There is at least one prime number’ and this is in turn equivalent to ‘Some thing is a prime number’. The verb ‘exist’, the verb (...) phrase ‘there is’ and the quantifier ‘some’ are treated as all playing similar roles, and these roles are made explicit in the standard common formalization of all three sentences by a single formula of first-order logic: ‘(∃ x )[P( x ) & N( x )]’, where ‘P( x )’ abbreviates ‘ x is prime’ and ‘N( x )’ abbreviates ‘ x is a number’. The logical quantifier ‘∃’ accordingly symbolizes in context the role played by the English words ‘exists’, ‘some’ and ‘there is’. (shrink)

We discuss the thesis formulated by Hintikka that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that to account for these phenomena, we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries. The main contribution of the paper is showing how we can add (...) structure to contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments. (shrink)