Results for 'basic propositional logic'

964 found
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  1.  37
    Basic propositional logic and the weak excluded middle.Majid Alizadeh & Mohammad Ardeshir - 2019 - Logic Journal of the IGPL 27 (3):371-383.
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  2.  36
    Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
    We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being E1, a theory axiomatized by T → ⊥. The intersection CPC ∩ E1 is axiomatizable by the Principle of the Excluded Middle A V ∨ ⌝A. If B (...)
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  3.  55
    On the linear Lindenbaum algebra of Basic Propositional Logic.Majid Alizadeh & Mohammad Ardeshir - 2004 - Mathematical Logic Quarterly 50 (1):65.
    We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra.
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  4.  85
    Gentzen-style axiomatizations for some conservative extensions of basic propositional logic.Mojtaba Aghaei & Mohammad Ardeshir - 2001 - Studia Logica 68 (2):263-285.
    We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.
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  5. A Bounded Translation of Intuitionistic Propositional Logic into Basic Propositional Logic.Mojtaba Aghaei & Mohammad Ardeshir - 2000 - Mathematical Logic Quarterly 46 (2):195-206.
    In this paper we prove a bounded translation of intuitionistic propositional logic into basic propositional logic. Our new theorem, compared with the translation theorem in [1], has the advantage that it gives an effective bound on the translation, depending on the complexity of formulas.
     
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  6.  56
    Basic Propositional Calculus II. Interpolation: II. Interpolation.Mohammad Ardeshir & Wim Ruitenburg - 2001 - Archive for Mathematical Logic 40 (5):349-364.
    Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such (...)
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  7.  45
    (2 other versions)The basic constructive logic for negation-consistency defined with a propositional falsity constant.José M. Méndez, Gemma Robles & Francisco Salto - 2007 - Bulletin of the Section of Logic 36 (1-2):45-58.
  8.  38
    Bounded arithmetic, propositional logic, and complexity theory.Jan Krajicek - 1995 - New York, NY, USA: Cambridge University Press.
    This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then (...)
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  9.  27
    Interpolation Property on Visser's Formal Propositional Logic.Majid Alizadeh & Masoud Memarzadeh - 2022 - Bulletin of the Section of Logic 51 (3):297-316.
    In this paper by using a model-theoretic approach, we prove Craig interpolation property for Formal Propositional Logic, FPL, Basic propositional logic, BPL and the uniform left-interpolation property for FPL. We also show that there are countably infinite extensions of FPL with the uniform interpolation property.
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  10.  24
    Propositional Logic for Infinitive Sentences.Nicola Spinelli - 2024 - Journal of Logic, Language and Information 33 (2):197-234.
    This paper is about sentences of form To be human is to be an animal, To live is to fight, etc. I call them ‘infinitive sentences’. I define an augmented propositional language able to express them and give a matrix-based semantics for it. I also give a tableau proof system, called IL for Infinitive Logic. I prove soundness, completeness and a few basic theorems.
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  11.  49
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):233-246.
    Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, (...)
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  12.  56
    A cut-free Gentzen formulation of basic propositional calculus.Kentaro Kikuchi & Katsumi Sasaki - 2003 - Journal of Logic, Language and Information 12 (2):213-225.
    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. (...)
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  13.  74
    Relationships between basic propositional calculus and substructural logics.Kentaro Kikuchi - 2001 - Bulletin of the Section of Logic 30 (1):15-20.
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  14.  40
    New sequent calculi for Visser's Formal Propositional Logic.Katsumasa Ishii - 2003 - Mathematical Logic Quarterly 49 (5):525.
    Two cut-free sequent calculi which are conservative extensions of Visser's Formal Propositional Logic are introduced. These satisfy a kind of subformula property and by this property the interpolation theorem for FPL are proved. These are analogies to Aghaei-Ardeshir's calculi for Visser's Basic Propositional Logic.
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  15.  10
    An Axiom System for Basic Hybrid Logic with Propositional Quantifiers.Patrick Blackburn, Torben Braüner & Julie Lundbak Kofod - 2023 - In Helle Hvid Hansen, Andre Scedrov & Ruy J. G. B. De Queiroz, Logic, Language, Information, and Computation: 29th International Workshop, WoLLIC 2023, Halifax, NS, Canada, July 11–14, 2023, Proceedings. Springer Nature Switzerland. pp. 118-134.
    We present an axiom system for basic hybrid logic extended with propositional quantifiers (a second-order extension of basic hybrid logic) and prove its (basic and pure) strong completeness with respect to general models.
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  16. The enduring scandal of deduction: is propositional logic really uninformative?Marcello D'Agostino & Luciano Floridi - 2009 - Synthese 167 (2):271-315.
    Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by (...)
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  17.  42
    Sequent Calculi for Visser's Propositional Logics.Kentaro Kikuchi & Ryo Kashima - 2001 - Notre Dame Journal of Formal Logic 42 (1):1-22.
    This paper introduces sequent systems for Visser's two propositional logics: Basic Propositional Logic (BPL) and Formal Propositional Logic (FPL). It is shown through semantical completeness that the cut rule is admissible in each system. The relationships with Hilbert-style axiomatizations and with other sequent formulations are discussed. The cut-elimination theorems are also demonstrated by syntactical methods.
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  18.  31
    Correspondence Analysis for Some Fragments of Classical Propositional Logic.Yaroslav Petrukhin & Vasilyi Shangin - 2021 - Logica Universalis 15 (1):67-85.
    In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in (...)
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  19.  74
    Propositional Content.Peter Hanks - 2015 - Oxford, United Kingdom: Oxford University Press.
    Peter Hanks defends a new theory about the nature of propositional content, according to which the basic bearers of representational properties are particular mental or spoken actions. He explains the unity of propositions and provides new solutions to a long list of puzzles and problems in philosophy of language.
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  20. A short note on intuitionistic propositional logic with multiple conclusions.Valéria de Paiva & Luiz Pereira - 2005 - Manuscrito 28 (2):317-329.
    A common misconception among logicians is to think that intuitionism is necessarily tied-up with single conclusion calculi. Single conclusion calculi can be used to model intuitionism and they are convenient, but by no means are they necessary. This has been shown by such influential textbook authors as Kleene, Takeuti and Dummett, to cite only three. If single conclusions are not necessary, how do we guarantee that only intuitionistic derivations are allowed? Traditionally one insists on restrictions on particular rules: implication right, (...)
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  21.  9
    A Propositional Cirquent Calculus for Computability Logic.Giorgi Japaridze - 2024 - Journal of Logic, Language and Information 33 (4):363-389.
    Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization  CL18 \text{ CL18 } CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The (...)
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  22.  17
    “Logical Lantern”: Analogue of the Square of Opposition for Propositions in V.I. Markin’s Universal Language for Traditional Positive Syllogistic Theories.Oksana Cherkashina - 2024 - Logica Universalis 18 (1):35-47.
    In this paper is constructed an analogue of the square of opposition for propositions about relations between two non-empty sets. Unlike the classical square of opposition, the proposed scheme uses all logically possible syllogistic constants, formulated in V.I. Markin’s universal language for traditional positive syllogistic theories. This scheme can be called “Logical lantern”. The basic constants of this language are representing the five basic relations between two non-empty sets: equity, strict inclusion, reversed strict inclusion, intersection and exclusion (considered (...)
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  23. (1 other version)The Undecidability of Propositional Adaptive Logic.Leon Horsten & Philip Welch - 2007 - Synthese 158 (1):41-60.
    We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set (...)
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  24.  82
    Structured propositions and the logical form of predication.Gary Ostertag - 2019 - Synthese 196 (4):1475-1499.
    Jeffrey King, Scott Soames, and others have recently challenged the familiar identification of a Russellian proposition, such as the proposition that Brutus stabbed Caesar, with an ordered sequence constructed out of objects, properties, and relations. There is, as they point out, a surplus of candidate sequences available that are each equally serviceable. If so, any choice among these candidates will be arbitrary. In this paper, I show that, unless a controversial assumption is made regarding the nature of nonsymmetrical relations, none (...)
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  25. A logical form for the propositional attitudes.Howard Burdick - 1982 - Synthese 52 (2):185 - 230.
    The author puts forth an approach to propositional attitude contexts based upon the view that one does not have beliefs of ordinary extensional entitiessimpliciter. Rather, one has beliefs of such entities as presented in various manners. Roughly, these are treated as beliefs of ordered pairs — the first member of which is the ordinary extensional entity and the second member of which is a predicate that it satisfies. Such an approach has no difficulties with problems involving identity, such as (...)
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  26.  29
    Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic.Roberto Cignoli & Antoni Torrens - 2003 - Archive for Mathematical Logic 42 (4):361-370.
    Using the theory of BL-algebras, it is shown that a propositional formula ϕ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ˜˜ϕ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ→˜φ)) → ψ, then ϕ is derivable in in classical logic if and only if ˜˜ ϕ is derivable in SBL. Axiomatic extensions of Basic (...)
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  27.  23
    Propositions and Paradoxes.Dustin Tucker - 2012 - Dissertation, University of Michigan
    Propositions are more than the bearers of truth and the meanings of sentences: they are also the objects of an array of attitudes including belief, desire, hope, and fear. This variety of roles leads to a variety of paradoxes, most of which have been sorely neglected. Arguing that existing work on these paradoxes is either too heavy-handed or too specific in its focus to be fully satisfactory, I develop a basic intensional logic and pursue and compare three strategies (...)
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  28. Expressivity of second order propositional modal logic.Balder ten Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.
    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 (...) and SOPML. (shrink)
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  29. Extensions of the basic constructive logic for weak consistency BKc1 defined with a falsity constant.Gemma Robles - 2007 - Logic and Logical Philosophy 16 (4):311-322.
    The logic BKc1 is the basic constructive logic for weak consistency in the ternary relational semantics without a set of designated points. In this paper, a number of extensions of B Kc1 defined with a propositional falsity constant are defined. It is also proved that weak consistency is not equivalent to negation-consistency or absolute consistency in any logic included in positive contractionless intermediate logic LC plus the constructive negation of BKc1 and the contraposition axioms.
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  30. Propositional dynamic logic as a logic of knowledge update and belief revision.Jan van Eijck - unknown
    This talk shows how propositional dynamic logic (PDL) can be interpreted as a logic for multi-agent knowledge update and belief revision, or as a logic of preference change, if the basic relations are read as preferences instead of plausibilities. Our point of departure is the logic of communication and change (LCC) of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their (...)
     
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  31.  44
    Propositional quantifiers in labelled natural deduction for normal modal logic.Matteo Pascucci - 2019 - Logic Journal of the IGPL 27 (6):865-894.
    This article concerns the treatment of propositional quantification in a framework of labelled natural deduction for modal logic developed by Basin, Matthews and Viganò. We provide a detailed analysis of a basic calculus that can be used for a proof-theoretic rendering of minimal normal multimodal systems with quantification over stable domains of propositions. Furthermore, we consider variations of the basic calculus obtained via relational theories and domain theories allowing for quantification over possibly unstable domains of propositions. (...)
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  32. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions.Martin Davis (ed.) - 1965 - Hewlett, NY, USA: Dover Publication.
    "A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers (...)
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  33.  21
    Propositional Q-Logic.Wolfl Stefan - 2002 - Journal of Philosophical Logic 31 (5):387-414.
    Topic of the paper is Q-logic – a logic of agency in its temporal and modal context. Q-logic may be considered as a basal logic of agency since the most important stit-operators discussed in the literature can be defined or axiomatized easily within its semantical and syntactical framework. Its basic agent dependent operator, the Q-operator (also known as Δ- or cstit-operator), which has been discussed independently by F. v. Kutschera and B. F. Chellas, is investigated (...)
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  34. Worlds and Propositions: The Structure and Ontology of Logical Space.Phillip Bricker - 1983 - Dissertation, Princeton University
    In sections 1 through 5, I develop in detail what I call the standard theory of worlds and propositions, and I discuss a number of purported objections. The theory consists of five theses. The first two theses, presented in section 1, assert that the propositions form a Boolean algebra with respect to implication, and that the algebra is complete, respectively. In section 2, I introduce the notion of logical space: it is a field of sets that represents the propositional (...)
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  35.  14
    Expressivity of Second Order Propositional Modal Logic.Balder Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.
    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 (...) and SOPML. (shrink)
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  36.  55
    Basic modal logic.John L. Pollock - 1967 - Journal of Symbolic Logic 32 (3):355-365.
    As anyone who is familiar with the literature knows, there is a great deal of controversy concerning which, if any, of the extant theories of propositional modal logic correctly formalizes the logic of certain logical concepts such as analyticity and logical necessity. Most of the controversy concerns certain principles that involve iterated modalities (where one modal operator occurs within the scope of another). For example, there is considerable disagreement about whether the principle(□p⊃□□p)should be considered valid. However, when (...)
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  37. Propositional q-logic.Stefan Wölfl - 2002 - Journal of Philosophical Logic 31 (5):387-414.
    Topic of the paper is Q-logic - a logic of agency in its temporal and modal context. Q-logic may be considered as a basal logic of agency since the most important stitoperators discussed in the literature can be defined or axiomatized easily within its semantical and syntactical framework. Its basic agent dependent operator, the Q-operator (also known as Δ- or cstit-operator), which has been discussed independently by E v. Kutschera and B. E Chellas, is investigated (...)
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  38. The Basic Intuitionistic Logic of Proofs.Sergei Artemov & Rosalie Iemhoff - 2007 - Journal of Symbolic Logic 72 (2):439 - 451.
    The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.
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  39.  70
    Neighborhood Semantics for Basic and Intuitionistic Logic.Morteza Moniri & Fatemeh Shirmohammadzadeh Maleki - 2015 - Logic and Logical Philosophy 24 (3):339-355.
    In this paper we present a neighborhood semantics for Intuitionistic Propositional Logic (IPL). We show that for each Kripke model of the logic there is a pointwise equivalent neighborhood model and vice versa. In this way, we establish soundness and completeness of IPL with respect to the neighborhood semantics. The relation between neighborhood and topological semantics are also investigated. Moreover, the notions of bisimulation and n-bisimulation between neighborhood models of IPL are defined naturally and some of their (...)
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  40.  91
    Free-variable tableaux for propositional modal logics.Bernhard Beckert & Rajeev GorÉ - 2001 - Studia Logica 69 (1):59-96.
    Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.
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  41. Propositions and the Substitution Anomaly.Steven E. Boër - 2009 - Journal of Philosophical Logic 38 (5):549-586.
    The Substitution Anomaly is the failure of intuitively coreferential expressions of the corresponding forms “that S” and “the proposition that S” to be intersubstitutable salva veritate under certain ‘selective’ attitudinal verbs that grammatically accept both sorts of terms as complements. The Substitution Anomaly poses a direct threat to the basic assumptions of Millianism, which predict the interchangeability of “that S” and “the proposition that S”. Jeffrey King has argued persuasively that the most plausible Millian solution is to treat the (...)
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  42.  10
    Outline of a Nominalist Theory of Propositions: An Essay in the Theory of Meaning and in the Philosophy of Logic.Paul Gochet - 1980 - Dordrecht, Netherland: Springer.
    1. IMPORTANCE OF THE SUBJECT In 1900, in A Critical Exposition of the Philosophy of Leihniz, Russell made the following assertion: "That all sound philosophy should begin with an analysis of propositions is a truth too evident, perhaps, to demand a proof". 1 Forty years later, the interest aroused by this notion had not decreased. C. J. Ducasse wrote in the Journal of Philosophy: "There is perhaps no question more basic for the theory of knowledge than that of the (...)
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  43. Why maps are not propositional.Elisabeth Camp - 2018 - In Alex Grzankowski & Michelle Montague, Non-Propositional Intentionality. Oxford, United Kingdom: Oxford University Press. pp. 19-45.
    A number of philosophers and logicians have argued for the conclusion that maps are logically tractable modes of representation by analyzing them in propositional terms. But in doing so, they have often left what they mean by "propositional" undefined or unjustified. I argue that propositions are characterized by a structure that is digital, universal, asymmetrical, and recursive. There is little positive evidence that maps exhibit these features. Instead, we can better explain their functional structure by taking seriously the (...)
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  44.  15
    Concept and object: the unity of the proposition in logic and psychology.Anthony Palmer - 1988 - New York: Routledge.
    What makes a visually appealing landscape? How can the design and use of a landscape be harmonised? In this significantly revised and updated third edition of Simon Bell's seminal text, he further explores the answers to these questions by interrogating a range of design principles, applications and ideas. Written for students, instructors and professionals, the book unveils a visual design vocabulary for anyone involved with landscape aesthetics including landscape architects, architects, planners, urban designers, landscape managers, foresters, geographers and ecologists. Structured (...)
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  45.  87
    Cn-definitions of propositional connectives.Witold A. Pogorzelski & Piotr Wojtylak - 2001 - Studia Logica 67 (1):1-26.
    We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.
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  46. Valuations for the Quantum Propositional Structures and Hidden Variables for Quantum Mechanics.Ariadna Chernavska - 1980 - Dissertation, The University of British Columbia (Canada)
    The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, where (...)
     
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  47.  14
    (1 other version)Logic: The Basics.Jc Beall - 2010 - New York: Routledge.
    _Logic: The Basics_ is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives (...)
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  48. Are There Ultimately Founded Propositions?Gregor Damschen - 2010 - Universitas Philosophica 27 (54):163-177.
    Can we find propositions that cannot rationally be denied in any possible world without assuming the existence of that same proposition, and so involving ourselves in a contradiction? In other words, can we find transworld propositions needing no further foundation or justification? Basically, three differing positions can be imagined: firstly, a relativist position, according to which ultimately founded propositions are impossible; secondly, a meta-relativist position, according to which ultimately founded propositions are possible but unnecessary; and thirdly, an absolute position, according (...)
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  49.  35
    Incompactness of the A1 Fragment of Basic Second Order Propositional Relevant Logic.Guillermo Badia - 2019 - Australasian Journal of Logic 16 (1):1-8.
    In this note we provide a simple proof of the incompactness over Routley-Meyer B-frames of the A1 fragment of the second order propositional relevant language.
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  50.  39
    KD45 with Propositional Quantifiers.P. Maurice Dekker - 2024 - Logic and Logical Philosophy 33 (1):27-54.
    Steinsvold (2020) has provided two semantics for the basic modal language enriched with propositional quantifiers (∀p). We define an extension EM of the system KD45_{\Box} and prove that EM is sound and complete for both semantics. It follows that the two semantics are equivalent.
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