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  1.  6
    Monotonicity Reasoning in the Age of Neural Foundation Models.Zeming Chen & Qiyue Gao - 2023 - Journal of Logic, Language and Information 33 (1):49-68.
    The recent advance of large language models (LLMs) demonstrates that these large-scale foundation models achieve remarkable capabilities across a wide range of language tasks and domains. The success of the statistical learning approach challenges our understanding of traditional symbolic and logical reasoning. The first part of this paper summarizes several works concerning the progress of monotonicity reasoning through neural networks and deep learning. We demonstrate different methods for solving the monotonicity reasoning task using neural and symbolic approaches and also discuss (...)
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  2.  16
    Capturing the Varieties of Natural Language Inference: A Systematic Survey of Existing Datasets and Two Novel Benchmarks.Reto Gubelmann, Ioannis Katis, Christina Niklaus & Siegfried Handschuh - 2023 - Journal of Logic, Language and Information 33 (1):21-48.
    Transformer-based Pre-Trained Language Models currently dominate the field of Natural Language Inference (NLI). We first survey existing NLI datasets, and we systematize them according to the different kinds of logical inferences that are being distinguished. This shows two gaps in the current dataset landscape, which we propose to address with one dataset that has been developed in argumentative writing research as well as a new one building on syllogistic logic. Throughout, we also explore the promises of ChatGPT. Our results show (...)
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  3.  11
    Monotonic Inference with Unscoped Episodic Logical Forms: From Principles to System.Gene Louis Kim, Mandar Juvekar, Junis Ekmekciu, Viet Duong & Lenhart Schubert - 2023 - Journal of Logic, Language and Information 33 (1):69-88.
    We describe the foundations and the systematization of natural logic-like monotonic inference using unscoped episodic logical forms (ULFs) that as reported by Kim et al. (Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA), Groningen, 2021a, b) introduced and first evaluated. In addition to providing a more detailed explanation of the theory and system, we present results from extending the inference manager to address a few of the limitations that as reported by Kim et al. (...)
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  4.  29
    Assessing the Strengths and Weaknesses of Large Language Models.Shalom Lappin - 2023 - Journal of Logic, Language and Information 33 (1):9-20.
    The transformers that drive chatbots and other AI systems constitute large language models (LLMs). These are currently the focus of a lively discussion in both the scientific literature and the popular media. This discussion ranges from hyperbolic claims that attribute general intelligence and sentience to LLMs, to the skeptical view that these devices are no more than “stochastic parrots”. I present an overview of some of the weak arguments that have been presented against LLMs, and I consider several of the (...)
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  5.  15
    A Computational Algebraic Analysis of Hindi Syntax.Alok Debanth & Manish Shrivastava - 2023 - Journal of Logic, Language and Information 32 (5):759-776.
    In this paper, we present a computational algebraic representation of Hindi syntax. This paper is the first attempt to establish the representation of various facets of Hindi syntax into algebra, including dual nominative/ergative behavior, a syntacto-semantic case system and complex agreement rules between the noun and verb phrase. Using the pregroup analysis framework, we show how we represent morphological type reduction for morphological behavior of lexical markers, the representation of causative constructions which are morphologically affixed, as well as of light (...)
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  6.  14
    A Logical Theory for Conditional Weak Ontic Necessity Based on Context Update.Fengkui Ju - 2023 - Journal of Logic, Language and Information 32 (5):777-807.
    Weak ontic necessity is the ontic necessity expressed by “should/ought to” in English. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds at the present world is irrelevant to whether its prejacent holds at the present world. In this paper, by combining premise semantics and update semantics for conditionals, we present a logical theory for conditional weak ontic necessity based on context update. A context is a set of (...)
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  7.  9
    Graph Grammar Formalism with Multigranularity for Spatial Graphs.Yufeng Liu, Fan Yang & Jian Liu - 2023 - Journal of Logic, Language and Information 32 (5):809-827.
    Traditional spatial enabled grammars lack flexibility in specifying the spatial semantics of graphs. This paper describes a new graph grammar formalism called the multigranularity Coordinate Graph Grammar (mgCGG) for spatial graphs. Based on the Coordinate Graph Grammar (CGG), the mgCGG divides coordinates into two categories, physical coordinates and grammatical coordinates, where physical coordinates are the common coordinates in the real world, and grammatical coordinates describe the restrictions on the spatial semantics. In the derivation and reduction of the mgCGG, the spatial (...)
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  8.  16
    Formal Modelling and Verification of Probabilistic Resource Bounded Agents.Hoang Nga Nguyen & Abdur Rakib - 2023 - Journal of Logic, Language and Information 32 (5):829-859.
    Many problems in Multi-Agent Systems (MASs) research are formulated in terms of the abilities of a coalition of agents. Existing approaches to reasoning about coalitional ability are usually focused on games or transition systems, which are described in terms of states and actions. Such approaches however often neglect a key feature of multi-agent systems, namely that the actions of the agents require resources. In this paper, we describe a logic for reasoning about coalitional ability under resource constraints in the probabilistic (...)
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  9.  12
    Double Negation as Minimal Negation.Satoru Niki - 2023 - Journal of Logic, Language and Information 32 (5):861-886.
    N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the (...)
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  10.  15
    Commutative Lambek Grammars.Tikhon Pshenitsyn - 2023 - Journal of Logic, Language and Information 32 (5):887-936.
    Lambek categorial grammars is a class of formal grammars based on the Lambek calculus. Pentus proved in 1993 that they generate exactly the class of context-free languages without the empty word. In this paper, we study categorial grammars based on the Lambek calculus with the permutation rule LP. Of particular interest is the product-free fragment of LP called the Lambek-van Benthem calculus LBC. Buszkowski in his 1984 paper conjectured that grammars based on the Lambek-van Benthem calculus (LBC-grammars for short) generate (...)
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  11.  18
    Modified Numerals and Split Disjunction: The First-Order Case.Maria Aloni & Peter van Ormondt - 2023 - Journal of Logic, Language and Information 32 (4):539-567.
    We present a number of puzzles arising for the interpretation of modified numerals. Following Büring and others we assume that the main difference between comparative and superlative modifiers is that only the latter convey disjunctive meanings. We further argue that the inference patterns triggered by disjunction and superlative modifiers are hard to capture in existing semantic and pragmatic analyses of these phenomena (neo-Gricean or grammatical alike), and we propose a novel account of these inferences in the framework of bilateral state-based (...)
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  12.  15
    Convexity and Monotonicity in Language Coordination: Simulating the Emergence of Semantic Universals in Populations of Cognitive Agents.Nina Gierasimczuk, Dariusz Kalociński, Franciszek Rakowski & Jakub Uszyński - 2023 - Journal of Logic, Language and Information 32 (4):569-600.
    Natural languages vary in their quantity expressions, but the variation seems to be constrained by general properties, so-calleduniversals. Their explanations have been sought among constraints of human cognition, communication, complexity, and pragmatics. In this article, we apply a state-of-the-art language coordination model to the semantic domain of quantities to examine whether two quantity universals—monotonicity and convexity—arise as a result of coordination. Assuming precise number perception by the agents, we evolve communicatively usable quantity terminologies in two separate conditions: a numeric-based condition (...)
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  13.  12
    On the Fundamental Role of ‘Means That’ in Semantic Theorizing.Teo Grünberg, David Grünberg & Oğuz Akçelik - 2023 - Journal of Logic, Language and Information 32 (4):601-656.
    Our aim is to illuminate the interconnected notions of meaning and truth. For this purpose, we investigate the relationship between meaning theories based on commonsensical ‘means that’ and interpretive truth theories. The latter are Tarski–Davidson-style truth theories serving as meaning theories. We consider analytically true semantic principles containing ‘means’ and ‘means that’ side to side with ‘denotes’, ‘satisfies’, and ‘true’, which constitute the extensional semantic constants of interpretive truth theories. We show that these semantic constants are definable in terms of (...)
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  14.  11
    Iterated AGM Revision Based on Probability Revision.Sven Ove Hansson - 2023 - Journal of Logic, Language and Information 32 (4):657-675.
    Close connections between probability theory and the theory of belief change emerge if the codomain of probability functions is extended from the real-valued interval [0, 1] to a hyperreal interval with the same limits. Full beliefs are identified as propositions with a probability at most infinitesimally smaller than 1. Full beliefs can then be given up, and changes in the set of full beliefs follow a pattern very close to that of AGM revision. In this contribution, iterated revision is investigated. (...)
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  15.  24
    From Counterfactual Conditionals to Temporal Conditionals.Yuichiro Hosokawa - 2023 - Journal of Logic, Language and Information 32 (4):677-706.
    Although it receives less attention, (Lewis in Noûs 13:455–476, 1979. https://doi.org/10.2307/2215339) admitted that the branching-time(-like) model fits a wide range of counterfactuals, including (Nix) ‘If Nixon had pressed the button, there would have been a nuclear war’, which was raised by (Fine in Mind 84:451–458, 1975). However, Lewis then claimed that similarity analysis is more general than temporality analysis. In this paper, we do not scrutinise his claim. Instead, we re-analyse (Nix) not only model-theoretically but also proof-theoretically from the ‘meaning-as-use’ (...)
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  16.  8
    Relativized Adjacency.Dakotah Lambert - 2023 - Journal of Logic, Language and Information 32 (4):707-731.
    For each class in the piecewise-local subregular hierarchy, a relativized (tier-based) variant is defined. Algebraic as well as automata-, language-, and model-theoretic characterizations are provided for each of these relativized classes, except in cases where this is provably impossible. These various characterizations are necessarily intertwined due to the well-studied logic-automaton connection and the relationship between finite-state automata and (syntactic) semigroups. Closure properties of each class are demonstrated by using automata-theoretic methods to provide constructive proofs for the closures that do hold (...)
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  17.  17
    Propositional Forms of Judgemental Interpretations.Tao Xue, Zhaohui Luo & Stergios Chatzikyriakidis - 2023 - Journal of Logic, Language and Information 32 (4):733-758.
    In formal semantics based on modern type theories, some sentences may be interpreted as judgements and some as logical propositions. When interpreting composite sentences, one may want to turn a judgemental interpretation or an ill-typed semantic interpretation into a proposition in order to obtain an intended semantics. For instance, an incorrect judgement $$a:A$$ may be turned into its propositional form $$\textsc {is}(A,a)$$ and an ill-typed application p(a) into $$\textsc {do}(p,a)$$, so that the propositional forms can take part in logical compositions (...)
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  18.  20
    Language Learnability in the Limit: A Generalization of Gold’s Theorem.Fernando C. Alves - 2023 - Journal of Logic, Language and Information 32 (3):363-372.
    In his pioneering work in the field of inductive inference, Gold (Inf Control 10:447–474, 1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not identifiable in the limit (learnable in the exact sense) from complete texts. Gold’s work paved the way for computational learning theories of language and has implications for two linguistically relevant classes in the Chomsky hierarchy (cf. Chomsky in Inf Control 2:137–167, 1959, Chomsky in Knowledge (...)
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  19.  10
    On $${{{\mathcal {F}}}}$$-Systems: A Graph-Theoretic Model for Paradoxes Involving a Falsity Predicate and Its Application to Argumentation Frameworks.Gustavo Bodanza - 2023 - Journal of Logic, Language and Information 32 (3):373-393.
    $${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the (...)
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  20.  15
    Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5.Norihiro Kamide - 2023 - Journal of Logic, Language and Information 32 (3):395-440.
    Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson’s constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved.
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  21.  8
    Some Remarks on Semantics and Expressiveness of the Sentential Calculus with Identity.Steffen Lewitzka - 2023 - Journal of Logic, Language and Information 32 (3):441-471.
    R. Suszko’s Sentential Calculus with Identity \( SCI \) results from classical propositional calculus \( CPC \) by adding a new connective \(\equiv \) and axioms for identity \(\varphi \equiv \psi \) (which we interpret here as ‘propositional identity’). We reformulate the original semantics of \( SCI \) using Boolean prealgebras which, introduced in different ways, are known in the literature as structures for the modeling of (hyper-) intensional semantics. We regard intensionality here as a measure for the discernibility of (...)
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  22.  21
    Names and Quantifiers: Bringing Them Together in Classical Logic.Jacek Paśniczek - 2023 - Journal of Logic, Language and Information 32 (3):473-487.
    Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting terms, can be accommodated in the new syntax as expressions suited to being subjects of sentences. In the light of this, a formal system that is an extension of classical first-order logic is developed here, and is (...)
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  23.  10
    Complexity of the Universal Theory of Residuated Ordered Groupoids.Dmitry Shkatov & C. J. Van Alten - 2023 - Journal of Logic, Language and Information 32 (3):489-510.
    We study the computational complexity of the universal theory of residuated ordered groupoids, which are algebraic structures corresponding to Nonassociative Lambek Calculus. We prove that the universal theory is co $$\textsf {NP}$$ -complete which, as we observe, is the lowest possible complexity for a universal theory of a non-trivial class of structures. The universal theories of the classes of unital and integral residuated ordered groupoids are also shown to be co $$\textsf {NP}$$ -complete. We also prove the co $$\textsf {NP}$$ (...)
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  24.  11
    A Modal Loosely Guarded Fragment of Second-Order Propositional Modal Logic.Gennady Shtakser - 2023 - Journal of Logic, Language and Information 32 (3):511-538.
    In this paper, we introduce a variant of second-order propositional modal logic interpreted on general (or Henkin) frames, \(SOPML^{\mathcal {H}}\), and present a decidable fragment of this logic, \(SOPML^{\mathcal {H}}_{dec}\), that preserves important expressive capabilities of \(SOPML^{\mathcal {H}}\). \(SOPML^{\mathcal {H}}_{dec}\) is defined as a _modal loosely guarded fragment_ of \(SOPML^{\mathcal {H}}\). We demonstrate the expressive power of \(SOPML^{\mathcal {H}}_{dec}\) using examples in which modal operators obtain (a) the epistemic interpretation, (b) the dynamic interpretation. \(SOPML^{\mathcal {H}}_{dec}\) partially satisfies the principle of (...)
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  25.  19
    Referentiality and Configurationality in the Idiom and the Phrasal Verb.Cem Bozşahin - 2023 - Journal of Logic, Language and Information 32 (2):175-207.
    Two positions of Bolinger, about synonymy and meaningfulness of words, point to significance of controlling the referentiality of word forms, from representing them in grammar to their projection onto surface structure, i.e. configurationality. In particular, it becomes critical to control the range of surface substitution for surface syntactic categories of words to maintain referential properties of idiosyncrasy. Categorial grammars as reference systems suggest ways to keep the two aspects in grammar. The first dividend of adopting a categorial perspective is systematically (...)
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  26.  20
    Some Notes on Dyadic Contingency.Jie Fan - 2023 - Journal of Logic, Language and Information 32 (2):209-217.
    In a recent work, Pizzi proposes a notion of dyadic non-contingency, and then gives an axiomatic system of dyadic non-contingency named \(\text {KD}\Delta ^2\), which is shown to be translationally equivalent to the deontic system KD and has the minimal system \(\text {K}\Delta \) of monadic contingency as a fragment. However, the reason why he defines dyadic non-contingency like that is unclear. In this article, inspired by the notion of relativized knowing-value in the literature, we give a plausible explanation for (...)
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  27.  41
    Algebraic Effects for Extensible Dynamic Semantics.Julian Grove & Jean-Philippe Bernardy - 2023 - Journal of Logic, Language and Information 32 (2):219-245.
    Research in dynamic semantics has made strides by studying various aspects of discourse in terms of computational effect systems, for example, monads (Shan, 2002; Charlow, 2014), Barker and 2014), (Maršik, 2016). We provide a system, based on graded monads, that synthesizes insights from these programs by formalizing individual discourse phenomena in terms of separate effects, or grades. Included are effects for introducing and retrieving discourse referents, non-determinism for indefiniteness, and generalized quantifier meanings. We formalize the behavior of individual effects, as (...)
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  28.  16
    Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.
    The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...)
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  29.  16
    Type Polymorphism, Natural Language Semantics, and TIL.Ivo Pezlar - 2023 - Journal of Logic, Language and Information 32 (2):275-295.
    Transparent intensional logic (TIL) is a well-explored type-theoretical framework for semantics of natural language. However, its treatment of polymorphic functions, which are essential for the analysis of various natural language phenomena, is still underdeveloped. In this paper, we address this issue and propose an extension of TIL that introduces polymorphism via type variables ranging over types and generalized variables ranging over constructions and types. Furthermore, we offer an analysis of sentences involving non-specific notional attitudes of the general form ‘_A_ considers (...)
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  30.  12
    A Substructural Approach to Explicit Modal Logic.Shawn Standefer - 2023 - Journal of Logic, Language and Information 32 (2):333–362.
    In this paper, we build on earlier work by Standefer (Logic J IGPL 27(4):543–569, 2019) in investigating extensions of substructural logics, particularly relevant logics, with the machinery of justification logics. We strengthen a negative result from the earlier work showing a limitation with the canonical model method of proving completeness. We then show how to enrich the language with an additional operator for implicit commitment to circumvent these problems. We then extend the logics with axioms for D, 4, and 5, (...)
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  31.  18
    Computable Heyting Algebras with Distinguished Atoms and Coatoms.Nikolay Bazhenov - 2023 - Journal of Logic, Language and Information 32 (1):3-18.
    The paper studies Heyting algebras within the framework of computable structure theory. We prove that the class _K_ containing all Heyting algebras with distinguished atoms and coatoms is complete in the sense of the work of Hirschfeldt et al. (Ann Pure Appl Logic 115(1-3):71-113, 2002). This shows that the class _K_ is rich from the computability-theoretic point of view: for example, every possible degree spectrum can be realized by a countable structure from _K_. In addition, there is no simple syntactic (...)
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  32.  13
    On the (Complete) Reasons Behind Decisions.Adnan Darwiche & Auguste Hirth - 2023 - Journal of Logic, Language and Information 32 (1):63-88.
    Recent work has shown that the input-output behavior of some common machine learning classifiers can be captured in symbolic form, allowing one to reason about the behavior of these classifiers using symbolic techniques. This includes explaining decisions, measuring robustness, and proving formal properties of machine learning classifiers by reasoning about the corresponding symbolic classifiers. In this work, we present a theory for unveiling the _reasons_ behind the decisions made by Boolean classifiers and study some of its theoretical and practical implications. (...)
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  33.  13
    Preface.Sujata Ghosh & R. Ramanujam - 2023 - Journal of Logic, Language and Information 32 (1):1-2.
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  34.  18
    Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems.Prosenjit Howlader & Mohua Banerjee - 2023 - Journal of Logic, Language and Information 32 (1):117-146.
    The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. (...)
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  35.  20
    Feferman–Vaught Decompositions for Prefix Classes of First Order Logic.Abhisekh Sankaran - 2023 - Journal of Logic, Language and Information 32 (1):147-174.
    The Feferman–Vaught theorem provides a way of evaluating a first order sentence \(\varphi \) on a disjoint union of structures by producing a decomposition of \(\varphi \) into sentences which can be evaluated on the individual structures and the results of these evaluations combined using a propositional formula. This decomposition can in general be non-elementarily larger than \(\varphi \). We introduce a “tree” generalization of the prenex normal form (PNF) for first order sentences, and show that for an input sentence (...)
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  36.  40
    Deontic Paradoxes in Mīmāṃsā Logics: There and Back Again.Kees van Berkel, Agata Ciabattoni, Elisa Freschi, Francesca Gulisano & Maya Olszewski - 2023 - Journal of Logic, Language and Information 32 (1):19-62.
    Centered around the analysis of the prescriptive portion of the Vedas, the Sanskrit philosophical school of Mīmāṃsā provides a treasure trove of normative investigations. We focus on the leading Mīmāṃsā authors Prabhākara, Kumārila and Maṇḍana, and discuss three modal logics that formalize their deontic theories. In the first part of this paper, we use logic to analyze, compare and clarify the various solutions to the _śyena_ controversy, a two-thousand-year-old problem arising from seemingly conflicting commands in the Vedas. In the second (...)
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