Since antiquity two different negations in natural languages have been noted: predicate negation (not honest) and predicate term negation (dishonest). The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two (not dishonest) and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.

Since antiquity two different negations in natural languages have been noted: predicate negation and predicate term negation . The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.

Is there a relation of logical consequence in natural language? Logicality, in the philosophical literature, has been conceived of as a restrictive phenomenon that is at odds with the unbridled richness and complexity of natural language. This article claims that there is a relation of logical consequence in natural language, and moreover, that it is the subject matter of the bulk of current theories of formal semantics. I employ the framework of _semantic constraints_ (Sagi (...) in Log Anal 57(227):259–276, 2014), which generalizes the Tarskian definition of logical consequence. I apply the widely accepted criterion of invariance under isomorphisms (Sher in J. Symb Log 61(2):653–686, 1996) generalized to the framework of semantic constraints (Sagi in Bull Symb Log 28(1):104–132, 2022b), combined with a theory of Glanzberg (in Metasemantics: new essays on the foundations of meaning, 2014) to delineate the relation of logical consequence in natural language. (shrink)

In his new book, Logical Form, Andrea Iacona distinguishes between two different roles that have been ascribed to the notion of logical form: the logical role and the semantic role. These two roles entail a bifurcation of the notion of logical form. Both notions of logical form, according to Iacona, are descriptive, having to do with different features of natural language sentences. I agree that the notion of logical form bifurcates, but not that the logical role is merely (...) descriptive. In this paper, I focus on formalization, a process by which logical form, on its logical role, is attributed to natural language sentences. According to some, formalization is a form of explication, and it involves normative, pragmatic, as well as creative aspects. I present a view by which formalization involves explicit commitments on behalf of a reasoner or an interpreter, which serve the normative grounds for the evaluation of a given text. In previous work, I proposed the framework of semantic constraints for the explication of logical consequence. Here, I extend the framework to include formalization constraints. The various constraints then serve the role of commitments. I discuss specific issues raised by Iacona concerning univocality, co-reference and equivocation, and I show how our views on these matters diverge as a result of our different starting assumptions. (shrink)

Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than ...

There has been a recent surge of work on deontic modality within philosophy of language. This work has put the deontic logic tradition in contact with natural language semantics, resulting in significant increase in sophistication on both ends. This chapter surveys the main motivations, achievements, and prospects of this work.

In June 22-27,1970, an International Working Symposium on Pragmatics of Natural Languages took place in Jerusalem under the auspices of The Israel Academy of Sciences and Humanities and the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science.! Some thirty philosophers, logicians, linguists, and psychologists from Israel, U.S.A., West-Germany, England, Belgium, France, Scotland, and Denmark met in seven formal and a number of informal sessions in order to discuss some (...) ofthe problems around the use and acquisition oflanguage which in the eyes of an increasing number of scholars have been left under treated in the recent upsurge ofinterest in theoretical linguistics and philos ophy of language. More specifically, during the formal sessions the following topics were discussed: The validity of the syntactics-seman tics-pragmatics trichotomy The present state of the competence-performance issue Logic and linguistics The New Rhetoric Speech acts Language acquisition. The participants in the Symposium distributed among themselves re prints and preprints of relevant material, partly in advance of the meeting, partly at its beginning. Each session was introduced by one or two modera tors, and summaries of each day's proceedings were prepared and distri buted the next day. The participants were invited to submit papers after the symposium, written under its impact. The eleven essays published here are the result. (shrink)

This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox and challenges classical logic and semantics. -/- The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of (...) sand, or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates. -/- Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case . (shrink)

Logicians have always found inspiration for new research in the ordinary language that is used on a daily basis and acquired naturally in childhood. Whereas the logical issues in the foundations of mathematics motivated the development of mathematical logic with its emphasis on notions of proof, validity, axiomatization, decidability, consistency, and completeness, the logical analysis of natural language motivated the development of philosophical logic with its emphasis on semantic notions of presupposition, entailment, modality, conditionals, and (...) intensionality. The relation between research programs in both mathematical and philosophical logic and natural language syntax and semantics as branches of theoretical linguistics has increased in importance throughout the last fifty years. This chapter reviews the development of one particularly interesting and lively area of interaction between formal logic and linguistics—the semantics of natural language. Research in this emergent field has proved fruitful for the development of empirically, cognitively adequate models of reasoning with partial information, sharing or exchanging information, dynamic interpretation in context, belief revision and other cognitive processes. (shrink)

In the first part of my paper I briefly present Jerzy Pelc’s functional approach to logical semiotics of natural language. This approach focuses on the use of natural language expressions and on its dependence on context and conversational situation. One of the important goals of this analysis is to appreciate the role of sentences in natural language and stress that it is by means of sentences that language fulfills its main roles. However, for (...) Pelc almost any expression can be used as a sentence, despite not being a grammatical sentence. In the second part I try to place Pelc’s standpoint within the framework of contemporary semantic minimalism – contextualism debate. I pay special attention to his treatment of subsentential expressions used to express propositions and argue that his view belongs to pragmatics-oriented approaches to subsentential speech acts. (shrink)

There are two kinds of logical errors. Either you use a non-valid scheme of an argument or your analysis of the premises is mistaken. No extensional or intensional theory can solve the following problem connected with analyzing NL expressions: The Leibniz principle of substituting identical for identical contains the condition a = b. Extensional as well as intensional systems (at least if intensions are defined as functions from possible worlds) analyzing this condition as formulated in natural language are (...) happy if a is contingently or logically or analytically equivalent with b, while this may be insufficient for applying Leibniz. Examples are adduced that show the absurdity of applying Leibniz in such cases. A following remedy is thinkable: one could try to formulate some axioms or perhaps meta-formulated rules that would eliminate the critical cases. This would mean however that a new theory came into being just to shield us from incorrectly applying Leibniz rule. Instead a procedural analysis of NL expressions is offered that makes it possible to unambiguously determine their sense and so their denotation in such a way that the above mentioned critical cases cannot set in. It is shown that the hyperintensional system defined by Transparent intensional logic is able to generally solve the main problems connected with using NL expressions. (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.

In this paper we present an approach to conditional reasoning tasks based on two main ideas. The first idea is that, in contrast with what is usually assumed, an ‘if… then…’ sentence is not an adequate translation in natural language of a logical formula containing a material implication as its principal operator. The second idea is that when subjects are required to check the validity of a sentence in a task, their inferences are not driven uniquely by the (...) content of the sentence, but also by other information embedded in the task scenario and, eventually, by their knowledge about the topic (i.e. information stored in memory). Data from 30 subjects tested on six different tasks are reported as evidence for our approach. The results show that conditional tasks are significantly more complex only when they are presented with ‘if… then…’ sentences and when the subject cannot rely on any extra information, such as contextual information or knowledge about the topic. (shrink)

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language (...) in its fundamental semantic charac. (shrink)

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching definitive conclusions.

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. (...) For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. (shrink)

We implement the extension of the logical consequence relation to a partial order ≤ on arbitary types built from e (entities) and t (Booleans) that was given in [1], and the definition of monotonicity preserving and monotonicity reversing functions in terms of ≤. Next, we present a new algorithm for polarity marking, and implement this for a particular fragment of syntax. Finally, we list the reseach agenda that these definitions and this algorithm suggest. The implementations use Haskell [8], and are (...) given in ‘literate programming’ style [9]. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation (...) into conditional connectives may show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Gödel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from (...) computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist. (shrink)

Before presenting the analysis of logical form of questions, I shall make some comments concerning questions in natural language. By utilizing examples of such questions I shall try to justify my conception of the semiotic function of questions and provide a basis for my analysis of their structure. One of the main aims of this chapter is to introduce definitions of erotetic concepts which I will use in the subsequent parts of the book and to sketch definitional connections (...) between elements of the erotetic conceptual scheme. (shrink)

This is a review of From Discourse to Logic: Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, written by Hans Kamp and Uwe Reyle and published by Kluwer Academic Publishers in 1993.

Transformer-based Pre-Trained Language Models currently dominate the field of Natural Language Inference (NLI). We first survey existing NLI datasets, and we systematize them according to the different kinds of logical inferences that are being distinguished. This shows two gaps in the current dataset landscape, which we propose to address with one dataset that has been developed in argumentative writing research as well as a new one building on syllogistic logic. Throughout, we also explore the promises of (...) ChatGPT. Our results show that our new datasets do pose a challenge to existing methods and models, including ChatGPT, and that tackling this challenge via fine-tuning yields only partly satisfactory results. (shrink)

Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its various (...) roles in conversation. This communicative turn in semantics raises historical questions: Why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural-language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand artificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural- language semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explana- tory priorities toward natural language itself rendered the adoption of the truth-conditional idealization inappropriate. Lifting the truth-conditional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology. (shrink)

_The Logic of Our Language_ teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences (...) into formal symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website. (shrink)