41 found

Year:

  1.  1
    Varieties of BL-Algebras II.P. Aglianò & F. Montagna - 2018 - Studia Logica 106 (4):721-737.
    In this paper we introduce a poset of subvarieties of BL-algebras, whose completion is the entire lattice of subvarietes; we exhibit also a description of this poset in terms of finite sequences of functions on the natural numbers.
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  2.  2
    Latarres, Lattices with an Arrow.Mohammad Ardeshir & Wim Ruitenburg - 2018 - Studia Logica 106 (4):757-788.
    A latarre is a lattice with an arrow. Its axiomatization looks natural. Latarres have a nontrivial theory which permits many constructions of latarres. Latarres appear as an end result of a series of generalizations of better known structures. These include Boolean algebras and Heyting algebras. Latarres need not have a distributive lattice.
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  3. Poset Product and BL-Chains.Manuela Busaniche & Conrado Gomez - 2018 - Studia Logica 106 (4):739-756.
    Different constructions of BL-chains are compared. We establish when the ordinal sum and the poset product of the same family of BL-chains coincide. We also compare the poset product of MV-chains and product chains with saturated BL-chains.
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  4. L -Hemi-Implicative Semilattices.José Luis Castiglioni & Hernán Javier San Martín - 2018 - Studia Logica 106 (4):675-690.
    An l-hemi-implicative semilattice is an algebra \\) such that \\) is a semilattice with a greatest element 1 and satisfies: for every \, \ implies \ and \. An l-hemi-implicative semilattice is commutative if if it satisfies that \ for every \. It is shown that the class of l-hemi-implicative semilattices is a variety. These algebras provide a general framework for the study of different algebras of interest in algebraic logic. In any l-hemi-implicative semilattice it is possible to define an (...)
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  5.  1
    Hereditarily Structurally Complete Superintuitionistic Deductive Systems.Alex Citkin - 2018 - Studia Logica 106 (4):827-856.
    Propositional logic is understood as a set of theorems defined by a deductive system: a set of axioms and a set of rules. Superintuitionistic logic is a logic extending intuitionistic propositional logic \. A rule is admissible for a logic if any substitution that makes each premise a theorem, makes the conclusion a theorem too. A deductive system \ is structurally complete if any rule admissible for the logic defined by \ is derivable in \. It is known that any (...)
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  6.  1
    Principal and Boolean Congruences on $$Varvec{}$$-Algebras.Aldo V. Figallo, Inés Inés Pascual & Gustavo Pelaitay - 2018 - Studia Logica 106 (4):857-882.
    The IKt-algebras were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. In this paper, our main interest is to investigate the principal and Boolean congruences on IKt-algebras. In order to do this we take into account a topological duality for these algebras obtained in Figallo et al. :673–701, 2017). Furthermore, we characterize Boolean and principal IKt-congruences and we show that Boolean IKt-congruence are principal IKt-congruences. Also, bearing in mind the (...)
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  7. Principal and Boolean Congruences on $$\Varvec{IKt}$$IKt-Algebras.Aldo V. Figallo, Inés Inés Pascual & Gustavo Pelaitay - 2018 - Studia Logica 106 (4):857-882.
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  8.  3
    Finitary Extensions of the Nilpotent Minimum Logic and Structural Completeness.Joan Gispert - 2018 - Studia Logica 106 (4):789-808.
    In this paper we study finitary extensions of the nilpotent minimum logic or equivalently quasivarieties of NM-algebras. We first study structural completeness of NML, we prove that NML is hereditarily almost structurally complete and moreover NM\, the axiomatic extension of NML given by the axiom \^{2}\leftrightarrow ^{2})^{2}\), is hereditarily structurally complete. We use those results to obtain the full description of the lattice of all quasivarieties of NM-algebras which allow us to characterize and axiomatize all finitary extensions of NML.
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  9.  10
    A Characterization of a Semimodular Lattice.Peng He & Xue-Ping Wang - 2018 - Studia Logica 106 (4):691-698.
    A geometric lattice is the lattice of closed subsets of a closure operator on a set which is zero-closure, algebraic, atomistic and which has the so-called exchange property. There are many profound results about this type of lattices, the most recent one of which, due to Czédli and Schimdt, says that a lattice L of finite length is semimodular if and only if L has a cover-preserving embedding into a geometric lattice G of the same length. The goal of our (...)
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  10.  2
    Massimiliano Carrara, Alexandra Arapinis and Friederike Moltmann , Unity and Plurality. Logic, Philosophy, and Linguistics, OUP: Oxford, 2016, Xv + 259 Pp., ISBN: 978-019-8716-32-7 £45, £36. [REVIEW]Giorgio Lando - 2018 - Studia Logica 106 (4):883-888.
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  11.  3
    General Extensional Mereology is Finitely Axiomatizable.Hsing-Chien Tsai - 2018 - Studia Logica 106 (4):809-826.
    Mereology is the theory of the relation “being a part of”. The first exact formulation of mereology is due to the Polish logician Stanisław Leśniewski. But Leśniewski’s mereology is not first-order axiomatizable, for it requires every subset of the domain to have a fusion. In recent literature, a first-order theory named General Extensional Mereology can be thought of as a first-order approximation of Leśniewski’s theory, in the sense that GEM guarantees that every definable subset of the domain has a fusion, (...)
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  12.  3
    First-Order Modal Logic: Frame Definability and a Lindström Theorem.R. Zoghifard & M. Pourmahdian - 2018 - Studia Logica 106 (4):699-720.
    We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that FML has (...)
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  13.  8
    Willem Conradie and Valentin Goranko, Logic and Discrete Mathematics: A Concise Introduction. Wiley, 2015, Pp. 450. ISBN-13: 978-1-118-75127-5 $42, ISBN-10: 978-1-118-75127-2 $37.99. [REVIEW]Torben Braüner - 2018 - Studia Logica 106 (3):671-673.
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  14.  6
    Eliciting Uncertainties: A Two Structure Approach.Timothy Childers & Ondrej Majer - 2018 - Studia Logica 106 (3):615-636.
    We recast subjective probabilities by rejecting behaviourist accounts of belief by explicitly distinguishing between judgements of uncertainty and expressions of those judgements. We argue that this entails rejecting that orderings of uncertainty be complete. This in turn leads naturally to several generalizations of the probability calculus. We define probability-like functions over incomplete algebras that reflect a subject’s incomplete judgements of uncertainty. These functions can be further generalized to inner and outer measures that reflect approximate elicitations.
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  15.  9
    Sequent Calculi for $${Mathsf {}}$$.Szymon Chlebowski - 2018 - Studia Logica 106 (3):541-563.
    In this paper we are applying certain strategy described by Negri and Von Plato :418–435, 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko’s Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.
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  16.  4
    Sequent Calculi for SCI.Szymon Chlebowski - 2018 - Studia Logica 106 (3):541-563.
    In this paper we are applying certain strategy described by Negri and Von Plato :418–435, 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko’s Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.
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  17.  4
    Truth, Partial Logic and Infinitary Proof Systems.Martin Fischer & Norbert Gratzl - 2018 - Studia Logica 106 (3):515-540.
    In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule.
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  18.  2
    Sequent Calculi for Semi-De Morgan and De Morgan Algebras.Minghui Ma & Fei Liang - 2018 - Studia Logica 106 (3):565-593.
    A contraction-free and cut-free sequent calculus \ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \ for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \ is embedded into \ via Gödel–Gentzen translation. \ is embedded into a sequent calculus for classical propositional logic. \ is embedded into the sequent calculus \ for intuitionistic (...)
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  19.  2
    Hintikka’s Independence-Friendly Logic Meets Nelson’s Realizability.Sergei P. Odintsov, Stanislav O. Speranski & Igor Yu Shevchenko - 2018 - Studia Logica 106 (3):637-670.
    Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump (...)
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  20. Reconstructing the Topology of the Elementary Self-Embedding Monoids of Countable Saturated Structures.Christian Pech & Maja Pech - 2018 - Studia Logica 106 (3):595-613.
    Every transformation monoid comes equipped with a canonical topology, the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This phenomenon is called automatic homeomorphicity. In this paper we show that whenever the automorphism group of a countable saturated structure has automatic homeomorphicity and a trivial center, then the monoid of elementary self-embeddings has automatic homeomorphicity, too. As a second result we strengthen a result by Lascar by showing (...)
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  21.  7
    Two Kinds of Consequential Implication.Claudio E. A. Pizzi - 2018 - Studia Logica 106 (3):453-480.
    The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength and \). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for (...)
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  22.  3
    Private Announcements on Topological Spaces.Hans van Ditmarsch, Sophia Knight & Aybüke Özgün - 2018 - Studia Logica 106 (3):481-513.
    In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information \, while all the other agents observe that group G is informed, but are uncertain whether the information provided is \ or \. This article follows up on our prior work where the dynamics were public events. We provide a complete axiomatization (...)
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  23.  5
    Semi-Intuitionistic Logic with Strong Negation.Juan Manuel Cornejo & Ignacio Viglizzo - 2018 - Studia Logica 106 (2):281-293.
    Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.
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  24.  2
    Ralf Schindler, Set Theory: Exploring Independence and Truth. Springer International Publishing, 2014, Pp. 332+X. ISBN: 978-3-319-06724-7 $79.99, ISBN: 978-3-319-06725-4 $59.99. [REVIEW]Vincenzo Dimonte - 2018 - Studia Logica 106 (2):449-452.
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  25.  9
    Gödel’s Natural Deduction.Kosta Došen & Miloš Adžić - 2018 - Studia Logica 106 (2):397-415.
    This is a companion to a paper by the authors entitled “Gödel on deduction”, which examined the links between some philosophical views ascribed to Gödel and general proof theory. When writing that other paper, the authors were not acquainted with a system of natural deduction that Gödel presented with the help of Gentzen’s sequents, which amounts to Jaśkowski’s natural deduction system of 1934, and which may be found in Gödel’s unpublished notes for the elementary logic course he gave in 1939 (...)
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  26.  8
    On Argumentation Logic and Propositional Logic.Antonis C. Kakas, Paolo Mancarella & Francesca Toni - 2018 - Studia Logica 106 (2):237-279.
    This paper studies the relationship between Argumentation Logic, a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic. In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of sentences in AL and Natural Deduction proofs of the complement of these sentences. The proof of this equivalence uses a restricted form (...)
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  27.  2
    Arithmetical Completeness Theorem for Modal Logic $$Mathsf{}$$.Taishi Kurahashi - 2018 - Studia Logica 106 (2):219-235.
    We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a \ provability predicate of T whose provability logic is precisely the modal logic \. For this purpose, we introduce a new bimodal logic \, and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for \.
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  28.  3
    Equivalences Among Polarity Algorithms.José-de-Jesús Lavalle-Martínez, Manuel Montes-Y.-Gómez, Luis Villaseñor-Pineda, Héctor Jiménez-Salazar & Ismael-Everardo Bárcenas-Patiño - 2018 - Studia Logica 106 (2):371-395.
    The concept of polarity is pervasive in natural language. It relates syntax, semantics and pragmatics narrowly, Semantics: an international handbook of natural language meaning, De Gruyter Mouton, Berlin, 2011; Israel in The grammar of polarity: pragmatics, sensitivity, and the logic of scales, Cambridge studies in linguistics, Cambridge University Press, Cambridge, 2014), it refers to items of many syntactic categories such as nouns, verbs and adverbs. Neutral polarity items appear in affirmative and negative sentences, negative polarity items cannot appear in affirmative (...)
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  29.  5
    Stone-Type Representations and Dualities for Varieties of Bisemilattices.Antonio Ledda - 2018 - Studia Logica 106 (2):417-448.
    In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes’ representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas–Dunn duality and introduce the categories of 2spaces and 2spaces\. The categories of 2spaces and 2spaces\ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces (...)
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  30.  11
    Interpolation in 16-Valued Trilattice Logics.Reinhard Muskens & Stefan Wintein - 2018 - Studia Logica 106 (2):345-370.
    In a recent paper we have defined an analytic tableau calculus \ for a functionally complete extension of Shramko and Wansing’s logic based on the trilattice \. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic—such as the relations Open image in new window, Open image in new window, and Open image in new window that each correspond to a lattice order in \; and Open image in new window, the intersection (...)
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  31. Propositional Epistemic Logics with Quantification Over Agents of Knowledge.Gennady Shtakser - 2018 - Studia Logica 106 (2):311-344.
    The paper presents a family of propositional epistemic logics such that languages of these logics are extended by quantification over modal operators or over agents of knowledge and extended by predicate symbols that take modal operators as arguments. Denote this family by \}\). There exist epistemic logics whose languages have the above mentioned properties :311–350, 1995; Lomuscio and Colombetti in Proceedings of ATAL 1996. Lecture Notes in Computer Science, vol 1193, pp 71–85, 1996). But these logics are obtained from first-order (...)
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  32.  6
    Deduction and Reduction Theorems for Inferential Erotetic Logic.Andrzej Wiśniewski - 2018 - Studia Logica 106 (2):295-309.
    The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.
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  33.  3
    Bisimulation for Conditional Modalities.A. Baltag & G. Cinà - 2018 - Studia Logica 106 (1):1-33.
    We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy–Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a series of (...)
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  34.  12
    Logic for Describing Strong Belief-Disagreement Between Agents.Jia Chen & Tianqun Pan - 2018 - Studia Logica 106 (1):35-47.
    The result of an interaction is influenced by its epistemic state, and several epistemic notions are related to multiagent situations. Strong belief-disagreement on a certain proposition between agents means that one agent believes the proposition and the other believes its negation. This paper presents a logical system describing strong belief-disagreement between agents and demonstrates its soundness and completeness. The notion of belief-disagreement as well as belief-agreement can facilitate gaining a clearer understanding of the acts of trade and speech.
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  35.  5
    A Second Pretabular Classical Relevance Logic.Asadollah Fallahi - 2018 - Studia Logica 106 (1):191-214.
    Pretabular logics are those that lack finite characteristic matrices, although all of their normal proper extensions do have some finite characteristic matrix. Although for Anderson and Belnap’s relevance logic R, there exists an uncountable set of pretabular extensions :1249–1270, 2008), for the classical relevance logic \\rightarrow B\}\) there has been known so far a pretabular extension: \. In Section 1 of this paper, we introduce some history of pretabularity and some relevance logics and their algebras. In Section 2, we introduce (...)
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  36.  6
    The Finite Model Property for Logics with the Tangle Modality.Robert Goldblatt & Ian Hodkinson - 2018 - Studia Logica 106 (1):131-166.
    The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness (...)
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  37.  6
    Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth.Carlo Nicolai - 2018 - Studia Logica 106 (1):101-130.
    We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...)
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  38.  4
    The Structure Group of a Generalized Orthomodular Lattice.Wolfgang Rump - 2018 - Studia Logica 106 (1):85-100.
    Orthomodular lattices with a two-valued Jauch–Piron state split into a generalized orthomodular lattice and its dual. GOMLs are characterized as a class of L-algebras, a quantum structure which arises in the theory of Garside groups, algebraic logic, and in connections with solutions of the quantum Yang–Baxter equation. It is proved that every GOML X embeds into a group G with a lattice structure such that the right multiplications in G are lattice automorphisms. Up to isomorphism, X is uniquely determined by (...)
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  39.  14
    Proof Theory for Functional Modal Logic.Shawn Standefer - 2018 - Studia Logica 106 (1):49-84.
    We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.
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  40.  10
    Correspondence Between Kripke Frames and Projective Geometries.Shengyang Zhong - 2018 - Studia Logica 106 (1):167-189.
    In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to (...)
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  41.  9
    Analyticity, Balance and Non-Admissibility of Cut in Stoic Logic.Susanne Bobzien & Roy Dyckhoff - 2018 - Studia Logica:1-23.
    This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a (...)
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