Search results for 'propositional copula' (try it on Scholar)

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  1. Proving in Finite Many-Valued Propositional (forthcoming). An Algorithm for Axiomatizing and Theorem Proving in Finite Many-Valued Propositional Logics* Walter A. Carnielli. Logique Et Analyse.score: 180.0
     
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  2. Paloma Pérez-Ilzarbe (2009). Jerónimo Pardo on the Unity of Mental Propositions. In J. Biard (ed.), Le langage mental du Moyen Âge à l'Âge Classique. Peeters Publishers.score: 82.0
    Originally motivated by a sophism, Pardo's discussion about the unity of mental propositions allows him to elaborate on his ideas about the nature of propositions. His option for a non-composite character of mental propositions is grounded in an original view about syncategorems: propositions have a syncategorematic signification, which allows them to signify aliquid aliqualiter, just by virtue of the mental copula, without the need of any added categorematic element. Pardo's general claim about the simplicity of mental propositions is developed (...)
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  3. Richard Gaskin (1995). Bradley's Regress, the Copula and the Unity of the Proposition. Philosophical Quarterly 45 (179):161-180.score: 60.0
    If we make the basic assumption that the components of a proposition have reference on the model of proper name and bearer, we face the problem of distinguishing the proposition from a mere list' of names. We neutralize the problem posed by that assumption of we first of all follow Wiggins and distinguish, in every predicate, a strictly predicative element (the copula), and a strictly non-predicative conceptual component (available to be quantified over). If we further allow the copula (...)
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  4. Richard Gaskin (2008). The Unity of the Proposition. Oxford University Press.score: 38.0
    Truth, falsity, and unity -- Sentences, lists, and collections -- Declarative and other kinds of sentence -- Declarative sentences and propositions -- Sentences, propositions, and truth-values -- Sentences, propositions, and unity -- Unity and complexity -- Reference and supposition -- Reference and signification -- Linguistic idealism and empirical realism -- Russell on truth, falsity, and unity (I) : 1903 -- Russell on truth, falsity, and unity (II) : 1910-13 -- Russell on truth, falsity, and unity (III) : 1918 -- Sense, (...)
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  5. Raul Corazzon, Abelard: Logic, Semantics, Ontology and His Theories of the Copula (Second Part).score: 30.0
    "With Abelard, the term 'copula' enters into western thought. In fact, although widely attested, the use of the term 'copula' in reference to Aristotle's work is totally anachronistic. (1) What led to this term? In his Dialectica, Abelard was mainly concerned with the way syllogisms can be construed. The interest of the copula was in fact derivative from this main concern. As Kneale and Kneale (The development of logic, 1962: 206) put it, 'it is clear that for (...)
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  6. Daniel Howard-Snyder (2013). Propositional Faith: What It is and What It is Not. American Philosophical Quarterly 50 (4):357-372.score: 24.0
    Reprinted in Philosophy of Religion: An Anthology, Wadsworth 2013, 6th edition, with an additional section entitled, "Reasons for the Common View," eds Michael Rea and Louis Pojman. What is propositional faith? At a first approximation, we might answer that it is the psychological attitude picked out by standard uses of the English locution “S has faith that p,” where p takes declarative sentences as instances, as in “He has faith that they’ll win”. Although correct, this answer is not nearly (...)
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  7. Sean Crawford (2014). Propositional or Non-Propositional Attitudes? Philosophical Studies 168 (1):179-210.score: 24.0
    Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such (...)
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  8. J. Adam Carter & Jesper Kallestrup (forthcoming). Extended Cognition and Propositional Memory. Philosophy and Phenomenological Research.score: 24.0
    The philosophical case for extended cognition is often made with reference to ‘extended-memory cases’ (e.g. Clark & Chalmers 1998); though, unfortunately, proponents of the hypothesis of extended cognition (HEC) as well as their adversaries have failed to appreciate the kinds of epistemological problems extended-memory cases pose for mainstream thinking in the epistemology of memory. It is time to give these problems a closer look. Our plan is as follows: in §1, we argue that an epistemological theory remains compatible with HEC (...)
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  9. John N. Williams (2008). Propositional Knowledge and Know-How. Synthese 165 (1):107 - 125.score: 24.0
    This paper is roughly in two parts. The first deals with whether know-how is constituted by propositional knowledge, as discussed primarily by Gilbert Ryle (1949) The concept of mind. London: Hutchinson, Jason Stanley and Timothy Williamson (2001). Knowing how. Journal of Philosophy, 98, pp. 411–444 as well as Stephen Hetherington (2006). How to know that knowledge-that is knowledge-how. In S. Hetherington (Ed.) Epistemology futures. Oxford: Oxford University Press. The conclusion of this first part is that know-how sometimes does and (...)
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  10. Timothy Schroeder (2006). Propositional Attitudes. Philosophy Compass 1 (1):65-73.score: 24.0
    The propositional attitudes are attitudes such as believing and desiring, taken toward propositions such as the proposition that snow flurries are expected, or that the Prime Minister likes poutine. Collectively, our views about the propositional attitudes make up much of folk psychology, our everyday theory of how the mind works.
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  11. Thomas Kelly (2002). The Rationality of Belief and Other Propositional Attitudes. Philosophical Studies 110 (2):163-96.score: 24.0
    In this paper, I explore the question of whether the expected consequences of holding a belief can affect the rationality of doing so. Special attention is given to various ways in which one might attempt to exert some measure of control over what one believes and the normative status of the beliefs that result from the successful execution of such projects. I argue that the lessons which emerge from thinking about the case ofbelief have important implications for the way we (...)
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  12. Mark E. Richard (1990). Propositional Attitudes: An Essay on Thoughts and How We Ascribe Them. New York: Cambridge University Press.score: 24.0
    This book makes a stimulating contribution to the philosophy of language and philosophy of mind. It begins with a spirited defense of the view that propositions are structured and that propositional structure is "psychologically real." The author then develops a subtle view of propositions and attitude ascription. The view is worked out in detail with attention to such topics as the semantics of conversations, iterated attitude ascriptions, and the role of propositions as bearers of truth. Along the way important (...)
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  13. Friederike Moltmann & Mark Textor (eds.) (forthcoming). Act-Based Conceptions of Propositional Content. Contemporary and Historical Perspectives. Oxford University Press.score: 24.0
    Ever since Frege, propositions have played a central role in philosophy of language. Propositions are generally conceived as abstract objects that have truth conditions essentially and fulfill both the role of the meaning of sentences and of the objects or content of propositional attitudes. More recently, the abstract conception of propositions has given rise to serious dissatisfaction among a number of philosophers, who have instead proposed a conception of propositional content based on cognitive acts (Hanks, Moltmann, Soames). This (...)
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  14. Robert M. Gordon (2007). Ascent Routines for Propositional Attitudes. Synthese 159 (2):151 - 165.score: 24.0
    An ascent routine (AR) allows a speaker to self-ascribe a given propositional attitude (PA) by redeploying the process that generates a corresponding lower level utterance. Thus, we may report on our beliefs about the weather by reporting (under certain constraints) on the weather. The chief criticism of my AR account of self-ascription, by Alvin Goldman and others, is that it covers few if any PA’s other than belief and offers no account of how we can attain reliability in identifying (...)
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  15. James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.score: 24.0
    Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore (...)
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  16. Tobias Hansson Wahlberg (2010). The Tenseless Copula in Temporal Predication. Erkenntnis 72 (2):267 - 280.score: 24.0
    In this paper I explore how the tenseless copula is to be interpreted in sentences of the form “ a is F at t ”, where “ a ” denotes a persisting, changeable object, “ F ” stands for a prima facie intrinsic property and “ t ” for a B-time. I argue that the interpretation of the copula depends on the logical role assigned to the time clause. Having rejected the idea that the time clause is to (...)
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  17. Robert J. Matthews (2007/2010). The Measure of Mind: Propositional Attitudes and Their Attribution. Oxford University Press.score: 24.0
    A prospective introduction -- The received view -- Troubles with the received view -- Are propositional attitudes relations? -- Foundations of a measurement-theoretic account of the attitudes -- The basic measurement-theoretic account -- Elaboration and explication of the proposed measurement-theoretic account.
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  18. John Dilworth & Dylan Sabo (2014). A Dual-Component View of Propositional Grasping. Erkenntnis 79 (3):511-522.score: 24.0
    On a traditional or default view of the grasping or understanding of a singular proposition by an individual, it is assumed to be a unitary or holistic activity. However, naturalistic views of cognition plausibly could analyze propositional thinking in terms of more than one distinctive functional stage of cognitive processing, suggesting at least the potential legitimacy of a non-unitary analysis of propositional grasping. We outline a novel dual-component view of this kind, and show that it is well supported (...)
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  19. David Landy (2005). Inside Doubt: On the Non-Identity of the Theory of Mind and Propositional Attitude Psychology. [REVIEW] Minds and Machines 15 (3-4):399-414.score: 24.0
    Eliminative materialism is a popular view of the mind which holds that propositional attitudes, the typical units of our traditional understanding, are unsupported by modern connectionist psychology and neuroscience, and consequently that propositional attitudes are a poor scientific postulate, and do not exist. Since our traditional folk psychology employs propositional attitudes, the usual argument runs, it too represents a poor theory, and may in the future be replaced by a more successful neurologically grounded theory, resulting in a (...)
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  20. William P. Bechtel & A. Abrahamson (1990). Beyond the Exclusively Propositional Era. Synthese 82 (2):223-53.score: 24.0
    Contemporary epistemology has assumed that knowledge is represented in sentences or propositions. However, a variety of extensions and alternatives to this view have been proposed in other areas of investigation. We review some of these proposals, focusing on (1) Ryle's notion of knowing how and Hanson's and Kuhn's accounts of theory-laden perception in science; (2) extensions of simple propositional representations in cognitive models and artificial intelligence; (3) the debate concerning imagistic versus propositional representations in cognitive psychology; (4) recent (...)
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  21. Craig French (2012). Does Propositional Seeing Entail Propositional Knowledge? Theoria 78 (2):115-127.score: 24.0
    In a 2010 article Turri puts forward some powerful considerations which suggest that Williamson's view of knowledge as the most general factive mental state is false. Turri claims that this view is false since it is false that if S sees that p, then S knows that p. Turri argues that there are cases in which (A) S sees that p but (B) S does not know that p. In response I offer linguistic evidence to suppose that in propositional (...)
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  22. Jeffrey C. King (forthcoming). Acquaintance, Singular Thought and Propositional Constituency. Philosophical Studies:1-18.score: 24.0
    In a recent paper, Armstrong and Stanley (Philos Stud 154:205–222, 2011) argue that despite being initially compelling, a Russellian account of singular thought has deep difficulties. I defend a certain sort of Russellian account of singular thought against their arguments. In the process, I spell out a notion of propositional constituency that is independently motivated and has many attractive features.
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  23. Robert Trueman (2011). Propositional Functions in Extension. Theoria 77 (4):292-311.score: 24.0
    In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. (...)
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  24. Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.score: 24.0
    Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that (...)
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  25. Claes Strannegård, Simon Ulfsbäcker, David Hedqvist & Tommy Gärling (2010). Reasoning Processes in Propositional Logic. Journal of Logic, Language and Information 19 (3):283-314.score: 24.0
    We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants (...)
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  26. Jan Almäng (2014). Perception, Non-Propositional Content and the Justification of Perceptual Judgments. Metaphysica 15 (1):1-23.score: 24.0
    It is often argued that for a perceptual experience to be able to justify perceptual judgments, the perceptual experience must have a propositional content. For, it is claimed, only propositions can bear logical relations such as implication to each other. In this paper, this claim is challenged. It is argued that whereas perceptions and judgments both have intentional content, their contents have different structures. Perceptual content does not have a propositional structure. Perceptions and judgments can nevertheless have the (...)
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  27. Michael J. Carroll (1976). On Interpreting the S5 Propositional Calculus: An Essay in Philosophical Logic. Dissertation, University of Iowascore: 24.0
    Discusses alternative interpretations of the modal operators, for the modal propositional logic S5.
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  28. Richard H. Feldman (1986). Davidson's Theory of Propositional Attitudes. Canadian Journal of Philosophy 16 (December):693-712.score: 24.0
    Donald davidson has proposed an account of indirect discourse that has been the subject of a great deal of discussion. Critics have contended that the theory saddles sentences in indirect discourse with implications they do not have, That the theory rests on an unsuitably obscure primitive notion that it cannot be extended to "de re" constructions and that it cannot be extended to sentences about other propositional attitudes such as belief. In this paper, I formulate davidson's theory more precisely (...)
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  29. Xinli Wang & Ling Xu (2009). The Propositional Vs. Hermeneutic Models of Cross-Cultural Understanding. South African Journal of Philosophy 28 (3):312-331.score: 24.0
    hat the author attempts to address in this paper is a Kantian question: not whether, but how is cross-cultural understanding possible? And specifically, what is a more effective approach for cross-cultural understanding? The answer lies in an analysis of two different models of cross-cultural understanding, that is, propositional and hermeneutic understanding. To begin with, the author presents a linguistic interpretation of culture, i.e., a culture as a linguistically formulated and transmitted symbolic system with its conceptual core as a scheme (...)
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  30. Chris J. Mitchell, Jan De Houwer & Peter F. Lovibond (2009). The Propositional Nature of Human Associative Learning. Behavioral and Brain Sciences 32 (2):183-198.score: 24.0
    The past 50 years have seen an accumulation of evidence suggesting that associative learning depends on high-level cognitive processes that give rise to propositional knowledge. Yet, many learning theorists maintain a belief in a learning mechanism in which links between mental representations are formed automatically. We characterize and highlight the differences between the propositional and link approaches, and review the relevant empirical evidence. We conclude that learning is the consequence of propositional reasoning processes that cooperate with the (...)
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  31. Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209-223.score: 24.0
    We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.
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  32. Morten H. Sørensen & Paweł Urzyczyn (2010). A Syntactic Embedding of Predicate Logic Into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (4):457-473.score: 24.0
    We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic propositional logic. (...)
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  33. Michael Morreau & Sarit Kraus (1998). Syntactical Treatments of Propositional Attitudes. Artificial Intelligence 106 (1):161-177.score: 24.0
    Syntactical treatments of propositional attitudes are attractive to artificial intelligence researchers. But results of Montague (1974) and Thomason (1980) seem to show that syntactical treatments are not viable. They show that if representation languages are sufficiently expressive, then axiom schemes characterizing knowledge and belief give rise to paradox. Des Rivières and Levesque (1988) characterize a class of sentences within which these schemes can safely be instantiated. These sentences do not quantify over the propositional objects of knowledge and belief. (...)
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  34. Shane J. Ralston, Operationalizing Propositions as Proposals: Reviving Interest in John Dewey's Theory of Propositional Form.score: 24.0
    Dewey and Russell's debate over the status of logic in the twentieth-century is, by now, well-trodden ground for scholarly inquiry. However, Dewey's novel theory of propositions, first articulated in his 1938 Logic: The Theory of Inquiry, has received comparatively less attention than the debate that touched upon it. The paucity of interest among philosophers of language is probably due to a variety of reasons, such as the theory's unorthodox character and, what at least appears to be, its naive simplicity when (...)
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  35. Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.score: 24.0
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  36. Konrad Zdanowski (2009). On Second Order Intuitionistic Propositional Logic Without a Universal Quantifier. Journal of Symbolic Logic 74 (1):157-167.score: 24.0
    We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a (...)
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  37. Robert Goldblatt & Tomasz Kowalski (2012). The Power of a Propositional Constant. Journal of Philosophical Logic (1):1-20.score: 24.0
    Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of (...)
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  38. Kentaro Kikuchi & Katsumi Sasaki (2003). A Cut-Free Gentzen Formulation of Basic Propositional Calculus. Journal of Logic, Language and Information 12 (2):213-225.score: 24.0
    We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem (...)
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  39. Philip Hugly & Charles Sayward (1976). Prior on Propositional Identity. Analysis 36 (4):182-184.score: 24.0
    Let A, B, C stand for sentences expressing propositions; let A be a component of C; let C A/B be just like C except for replacing some occurrence of A in C by an occurrence of B; let = be a binary connective for propositional identity read as ‘the proposition that __ is the very same proposition as …’. Then authors defend adding ‘from C = C A/B infer A = B’ to Prior’s rules for propositional identity, appearing (...)
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  40. Adam Morton (2009). From Tracking Relations to Propositional Attitudes. European Journal of Analytic Philosophy 5 (2):7-18.score: 24.0
    I explore the possibility that propositional attitudes are not basic in folk psychology, and that what we really ascribe to people are relations to individuals, those that the apparently propositional contents of beliefs, desires, and other states concern. In particular, the relation between a state and the individuals that it tracks shows how ascription of propositional attitudes could grow out of ascription of relations between people and objects.
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  41. Charles Sayward & Philip Hugly (1979). More on Propositional Identity. Analysis 39 (3):129-132.score: 24.0
    We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (...)
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  42. Rohan French (2012). Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants. Notre Dame Journal of Formal Logic 53 (4):549-556.score: 24.0
    We show that there are denumerably many Post-complete normal modal logics in the language which includes an additional propositional constant. This contrasts with the case when there is no such constant present, for which it is well known that there are only two such logics.
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  43. Michael Kaminski & Nissim Francez (2014). Relational Semantics of the Lambek Calculus Extended with Classical Propositional Logic. Studia Logica 102 (3):479-497.score: 24.0
    We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
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  44. Søren Harnow Klausen (2008). The Phenomenology of Propositional Attitudes. Phenomenology and the Cognitive Sciences 7 (4):445-462.score: 24.0
    Propositional attitudes are often classified as non-phenomenal mental states. I argue that there is no good reason for doing so. The unwillingness to view propositional attitudes as being essentially phenomenal stems from a biased notion of phenomenality, from not paying sufficient attention to the idioms in which propositional attitudes are usually reported, from overlooking the considerable degree to which different intentional modes can be said to be phenomenologically continuous, and from not considering the possibility that propositional (...)
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  45. Peter Schroeder-Heister (2014). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica 102 (6):1185-1216.score: 24.0
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of introduction rules a (...)
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  46. M. W. Bunder & R. M. Rizkalla (2009). Proof-Finding Algorithms for Classical and Subclassical Propositional Logics. Notre Dame Journal of Formal Logic 50 (3):261-273.score: 24.0
    The formulas-as-types isomorphism tells us that every proof and theorem, in the intuitionistic implicational logic $H_\rightarrow$, corresponds to a lambda term or combinator and its type. The algorithms of Bunder very efficiently find a lambda term inhabitant, if any, of any given type of $H_\rightarrow$ and of many of its subsystems. In most cases the search procedure has a simple bound based roughly on the length of the formula involved. Computer implementations of some of these procedures were done in Dekker. (...)
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  47. Alessandro Capone (2013). The Pragmatics of Pronominal Clitics and Propositional Attitudes. Intercultural Pragmatics 10 (3):459-485.score: 24.0
    pronominal clitics, pragmatics and propositional attitudes.
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  48. Philip Hugly & Charles Sayward (1979). More on Propositional Identity. Analysis 39 (3):129-132.score: 24.0
    We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (...)
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  49. Jan Krajiček (1994). Lower Bounds to the Size of Constant-Depth Propositional Proofs. Journal of Symbolic Logic 59 (1):73-86.score: 24.0
    LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and $\bigwedge, \bigvee$ (both of bounded arity). Then for every d ≥ 0 and n ≥ 2, there is a set Td n of depth d sequents of total size O(n3 + d) which are refutable in LK by depth d + 1 proof of size exp(O(log2 n)) but such that every depth d refutation must have the size at least exp(nΩ(1)). The sets Td (...)
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  50. Philip Hugly & Charles Sayward (1981). Completeness Theorems for Two Propositional Logics in Which Identity Diverges From Mutual Entailment. Notre Dame Journal of Formal Logic 22 (3):269-282.score: 24.0
    Anderson and Belnap devise a model theory for entailment on which propositional identity equals proposional coentailment. This feature can be reasonably questioned. The authors devise two extensions of Anderson and Belnap’s model theory. Both systems preserve Anderson and Belnap’s results for entailment, but distinguish coentailment from identity.
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