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About this topic
Summary This miscellaneous leaf node is mostly used for the biconditional or material equivalence; it is also used for any other linguistic connective that is not clearly a negation, conjunction, disjunction, or some form of conditional. The top category, "Connectives," although not a leaf node, is appropriate for discussions of connectives generally or collectively or for discussions of several of them in a single work.
Key works Each connective has separate key works.
Introductions Each connective has separate introductory works, which are either comprehensive, or included in standard logic textbooks which provide introductions to all of them, normally (but not always) adopting the truth-functional view, although (often) explaining that there are alternative views, and sometimes briefly listing or discussing (some of) them.
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  1. Ken Akiba (2009). A New Theory of Quantifiers and Term Connectives. Journal of Logic, Language and Information 18 (3):403-431.
    This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys (...)
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  2. Patrícia Amaral & Fabio Del Prete (2010). Approximating the Limit: The Interaction Between Quasi 'Almost' and Some Temporal Connectives in Italian. [REVIEW] Linguistics and Philosophy 33 (2):51-115.
    This paper focuses on the interpretation of the Italian approximative adverb quasi ‘almost’ by primarily looking at cases in which it modifies temporal connectives, a domain which, to our knowledge, has been largely unexplored thus far. Consideration of this domain supports the need for a scalar account of the semantics of quasi (close in spirit to Hitzeman’s semantic analysis of almost, in: Canakis et al. (eds) Papers from the 28th regional meeting of the Chicago Linguistic Society, 1992). When paired with (...)
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  3. Irving H. Anellis (2011). Peirce's Truth-Functional Analysis and the Origin of the Truth Table. History and Philosophy of Logic 33 (1):87 - 97.
    We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...)
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  4. Sigrid Beck (2000). The Semantics of Different: Comparison Operator and Relational Adjective. [REVIEW] Linguistics and Philosophy 23 (2):101-139.
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  5. Patrick Blackburn & Maarten Marx (2002). Remarks on Gregory's “Actually” Operator. Journal of Philosophical Logic 31 (3):281-288.
    In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an "actually" operator with the work of Arthur Prior now known under (...)
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  6. A. J. Dale (1982). Material Equivalence and Tautological Entailment. Notre Dame Journal of Formal Logic 23 (4):435-442.
  7. Charles B. Daniels (1987). “The Story Says That” Operator in Story Semantics. Studia Logica 46 (1):73 - 86.
    <span class='Hi'></span> In <span class='Hi'></span>[2]<span class='Hi'></span> a semantics for implication is offered that makes use of stories <span class='Hi'></span>— sets of sentences assembled under various constraints.<span class='Hi'></span> Sentences are evaluated at an actual world and in each member of a set of stories.<span class='Hi'></span> A sentence B is true in a story s just when B s.<span class='Hi'></span> A implies B iff for all stories and the actual world,<span class='Hi'></span> whenever A is true,<span class='Hi'></span> B is true.<span class='Hi'></span> In this (...)
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  8. Fabio Del Prete (2008). A Non-Uniform Semantic Analysis of the Italian Temporal Connectives Prima and Dopo. Natural Language Semantics 16 (2):157-203.
    In this paper, I argue that the temporal connective prima (‘before’) is a comparative adverb. The argument is based on a number of grammatical facts from Italian, showing that there is an asymmetry between prima and dopo (‘after’). On the ground of their divergent behaviour, I suggest that dopo has a different grammatical status from prima. I propose a semantic treatment for prima that is based on an independently motivated analysis of comparatives which can be traced back to Seuren (in: (...)
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  9. Branden Fitelson, Notes on Gibbard's Theorem.
    Let L be a sentential (object) language containing atoms ‘A’, ‘B’, . . . , and two logical connectives ‘&’ and ‘→’. In addition to these two logical connectives, L will also contain another binary connective ‘ ’, which is intended to be interpreted as the English indicative. In the meta-language for L , we will have two meta-linguistic operations: ‘ ’ and ‘ ’. ‘ ’ is a binary relation between individual sentences in L . It will be interpreted (...)
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  10. K. Forbes-Riley (2005). Computing Discourse Semantics: The Predicate-Argument Semantics of Discourse Connectives in D-LTAG. Journal of Semantics 23 (1):55-106.
    D-LTAG is a discourse-level extension of lexicalized tree-adjoining grammar (LTAG), in which discourse syntax is projected by different types of discourse connectives and discourse interpretation is a product of compositional rules, anaphora resolution, and inference. In this paper, we present a D-LTAG extension of ongoing work on an LTAG syntax-semantic interface. First, we show how predicate-argument semantics are computed for standard, ‘structural’ discourse connectives. These are connectives that retrieve their semantic arguments from their D-LTAG syntactic tree. Then we focus on (...)
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  11. Joseph S. Fulda (2005). A Pragmatic, Truth-Functional Solution to a Logical Difficulty with Biconditionals Absent in Conditionals. Journal of Pragmatics 37 (9/12):1419-1425/2120.
    Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original sense; only (...)
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  12. Joseph S. Fulda (1993). Exclusive Disjunction and the Biconditional: An Even-Odd Relationship. Mathematics Magazine 66 (2):124.
    Proves two simple identities relating the biconditional and exclusive disjunction. -/- The PDF has been made available gratis by the publisher.
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  13. Dov M. Gabbay (1972). A General Theory of the Conditional in Terms of a Ternary Operator. Theoria 38 (3):97-104.
  14. Michael Glanzberg (2011). More on Operators and Tense. [REVIEW] Analysis 71 (1):112 - 123.
    Cappelen and Hawthorne’s Relativism and Monadic Truth (2009) offers an extended defense of a thesis they call simplicity, which, in brief, holds that propositions are true or false simpliciter. Propositions are cast in their traditional roles as the contents of assertions, and as the semantic values of declarative sentences in contexts. Simplicity stands in sharp contrast to forms of relativism including, for instance, a form that hold that our claims are true or false only relative to a judge. This applies (...)
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  15. Dinda L. Gorlée (2008). Jakobson and Peirce. Sign Systems Studies 36 (2):341-373.
    Metalinguistic operations signify understanding and translation, specified in Jakobson’s varieties of six language functions and his three types of translation. Both models were first presented in the 1950s. This article is rooted in Jakobson’s models in connection with Peirce’s three categories. Bühler’s three functions with qualitative difference anticipated, perhaps not accidentally, Jakobson’s distinctions indicating qualitative difference within literary forms and structures as well as other fine arts. The semiotic discovery, criticism and perspective of elements and code-units settle the numerical differences (...)
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  16. Allen Hazen (1978). The Eliminability of the Actuality Operator in Propositional Modal Logic. Notre Dame Journal of Formal Logic 19 (4):617-622.
  17. Philip Hugly & Charles Sayward (1984). Do We Need Quantification? Notre Dame Journal of Formal Logic 25 (4):289-302.
    The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can (...)
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  18. Nathan Klinedinst & Daniel Rothschild (2012). Connectives Without Truth Tables. Natural Language Semantics 20 (2):137-175.
    There are certain uses of and and or that cannot be explained by their normal meanings as truth-functional connectives, even with sophisticated pragmatic resources. These include examples such as The cops show up, and a fight will break out (‘If the cops show up, a fight will break out’), and I have no friends, or I would throw a party (‘I have no friends. If I did have friends, I would throw a party.’). We argue that these uses are indeed (...)
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  19. Richard K. Larson (1988). Scope and Comparatives. Linguistics and Philosophy 11 (1):1 - 26.
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  20. C. Lewy (1946). Equivalence and Identity. Mind 55 (219):223-233.
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  21. Gerald J. Massey (1977). Negation, Material Equivalence, and Conditioned Nonconjunction: Completeness and Duality. Notre Dame Journal of Formal Logic 18 (1):140-144.
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  22. Robert K. Meyer (2008). Ai, Me and Lewis (Abelian Implication, Material Equivalence and C I Lewis 1920). Journal of Philosophical Logic 37 (2):169 - 181.
    C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. (...)
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  23. Ulrich Meyer (2013). Counterpart Theory and the Actuality Operator. Mind 122 (485):27-42.
    Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.
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  24. T. Nyan (1999). Simplement, as a Metalinguistic Operator. Argumentation 13 (3):275-295.
    This paper aims to provide a description of a metalinguistic use of simplement, one which occurs primarily in ce n'est pas que P simplement Q constructions. The two main points that will be raised concern the nature and function of the negation preceding P, and the meaning of simplement, which, following Anscombre and Ducrot, I will construe in procedural terms.
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  25. Sergei P. Odintsov (2006). Absurdity as Unary Operator. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):225-242.
    It was shown in the previous work of the author that one can avoid the paradox of minimal logic { ϕ , ¬ ϕ } ¬ ψ defining the negation operator via reduction not a constant of absurdity, but to a unary operator of absurdity. In the present article we study in details what does it mean that negation in a logical system can be represented via an absurdity or contradiction operator. We distinguish different sorts of such presentations. Finally, we (...)
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  26. Andrzej Pietruszczak (2006). On Applications of Truth-Value Connectives for Testing Arguments with Natural Connectives. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):143-156.
    In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first (...)
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  27. A. N. Prior (1969). Propositional Calculus in Implication and Non-Equivalence. Notre Dame Journal of Formal Logic 10 (3):271-272.
  28. Kjell Johan Saeboe (2001). The Semantics of Scandinavian Free Choice Items. Linguistics and Philosophy 24 (6):737-788.
    I present an analysis of Free Choice Items (FCIs), based on Scandinavian, where FCIs are complex and distinct from polarity sensitive items. Scandinavian FCIs are argued to have two components. One is a universal quantifying into modal contexts. The other is an operator mapping a type (s,t) expression onto itself, adjoining to the closest type t or (s,t) expression. Thus invoking Intensional Functional Application, this operator requires the presence of a modal in the scope of the universal quantifier. Facts concerning (...)
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  29. Yannis Stephanou (2005). First-Order Modal Logic with an 'Actually' Operator. Notre Dame Journal of Formal Logic 46 (4):381-405.
    In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas others (...)
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  30. Yael Sygal & Shuly Wintner (2009). Associative Grammar Combination Operators for Tree-Based Grammars. Journal of Logic, Language and Information 18 (3):293-316.
    Polarized unification grammar (PUG) is a linguistic formalism which uses polarities to better control the way grammar fragments interact. The grammar combination operation of PUG was conjectured to be associative. We show that PUG grammar combination is not associative, and even attaching polarities to objects does not make it order-independent. Moreover, we prove that no non-trivial polarity system exists for which grammar combination is associative. We then redefine the grammar combination operator, moving to the powerset domain, in a way that (...)
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  31. Isabel Gómez Txurruka (2003). The Natural Language Conjunction And. Linguistics and Philosophy 26 (3):255-285.
    In the first part of this article, we show that, contrary to the Gricean tradition, inter-clausal and is not semantically equivalent to logical conjunction and, contrary to temporal approaches such as Bar-Levand Palacas 1980, it is not temporallyloaded. We then explore a commonsenseidea – namely that while sentence juxtaposition might be interpreted either as discourse coordination or subordination, and indicates coordination. SDRT already includes notions of coordinating and subordinating discourse relations (cf. Lascarides and Asher 1993, Asher 1993), and the meaning (...)
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  32. Pascal Wagner-Egger (2007). Conditional Reasoning and the Wason Selection Task: Biconditional Interpretation Instead of Reasoning Bias. Thinking and Reasoning 13 (4):484 – 505.
    Two experiments were conducted to show that the IF … THEN … rules used in the different versions of Wason's (1966) selection task are not psychologically—though they are logically—equivalent. Some of these rules are considered by the participants as strict logical conditionals, whereas others are interpreted as expressing a biconditional relationship. A deductive task was used jointly with the selection task to show that the original abstract rule is quite ambiguous in this respect, contrary to deontic rules: the typical “error” (...)
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  33. Seth Yalcin (2010). Probability Operators. Philosophy Compass 5 (11):916-37.
    This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.
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