27 found
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  1.  16
    Logics for the relational syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
    The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio (...)
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  2.  7
    Handbook of Spatial Logics.Marco Aiello, Ian Pratt-Hartmann & Johan van Benthem (eds.) - 2007 - Springer Verlag.
    A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fields as Artificial Intelligence, Database Theory, Physics, and Philosophy. The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each (...)
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  3.  14
    Fragments of language.Ian Pratt-Hartmann - 2004 - Journal of Logic, Language and Information 13 (2):207-223.
    By a fragment of a natural language we mean a subset of thatlanguage equipped with semantics which translate its sentences intosome formal system such as first-order logic. The familiar conceptsof satisfiability and entailment can be defined for anysuch fragment in a natural way. The question therefore arises, for anygiven fragment of a natural language, as to the computational complexityof determining satisfiability and entailment within that fragment. Wepresent a series of fragments of English for which the satisfiabilityproblem is polynomial, NP-complete, EXPTIME-complete,NEXPTIME-complete (...)
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  4.  13
    The Hamiltonian Syllogistic.Ian Pratt-Hartmann - 2011 - Journal of Logic, Language and Information 20 (4):445-474.
    This paper undertakes a re-examination of Sir William Hamilton’s doctrine of the quantification of the predicate . Hamilton’s doctrine comprises two theses. First, the predicates of traditional syllogistic sentence-forms contain implicit existential quantifiers, so that, for example, All p is q is to be understood as All p is some q . Second, these implicit quantifiers can be meaningfully dualized to yield novel sentence-forms, such as, for example, All p is all q . Hamilton attempted to provide a deductive system (...)
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  5.  5
    Complexity of the two-variable fragment with counting quantifiers.Ian Pratt-Hartmann - 2005 - Journal of Logic, Language and Information 14 (3):369-395.
    The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.
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  6.  21
    On the computational complexity of the numerically definite syllogistic and related logics.Ian Pratt-Hartmann - 2008 - Bulletin of Symbolic Logic 14 (1):1-28.
    The numerically definite syllogistic is the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. The numerically definite relational syllogistic is the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= finite (...)
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  7.  2
    More Fragments of Language.Ian Pratt-Hartmann & Allan Third - 2006 - Notre Dame Journal of Formal Logic 47 (2):151-177.
    By a fragment of a natural language, we understand a collection of sentences forming a naturally delineated subset of that language and equipped with a semantics commanding the general assent of its native speakers. By the semantic complexity of such a fragment, we understand the computational complexity of deciding whether any given set of sentences in that fragment represents a logically possible situation. In earlier papers by the first author, the semantic complexity of various fragments of English involving at most (...)
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  8.  12
    The Syllogistic with Unity.Ian Pratt-Hartmann - 2013 - Journal of Philosophical Logic 42 (2):391-407.
    We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.
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  9.  7
    Temporal prepositions and their logic.Ian Pratt-Hartmann - 2005 - Artificial Intelligence 166 (1-2):1-36.
  10.  8
    A Topological Constraint Language with Component Counting.Ian Pratt-Hartmann - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):441-467.
    A topological constraint language is a formal language whose variables range over certain subsets of topological spaces, and whose nonlogical primitives are interpreted as topological relations and functions taking these subsets as arguments. Thus, topological constraint languages typically allow us to make assertions such as “region V1 touches the boundary of region V2”, “region V3 is connected” or “region V4 is a proper part of the closure of region V5”. A formula f in a topological constraint language is said to (...)
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  11.  12
    The fluted fragment revisited.Ian Pratt-Hartmann, Wiesław Szwast & Lidia Tendera - 2019 - Journal of Symbolic Logic 84 (3):1020-1048.
    We study the fluted fragment, a decidable fragment of first-order logic with an unbounded number of variables, motivated by the work of W. V. Quine. We show that the satisfiability problem for this fragment has nonelementary complexity, thus refuting an earlier published claim by W. C. Purdy that it is in NExpTime. More precisely, we consider ${\cal F}{{\cal L}^m}$, the intersection of the fluted fragment and the m-variable fragment of first-order logic, for all $m \ge 1$. We show that, for (...)
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  12.  28
    Quine’s fluted fragment revisited.Ian Pratt-Hartmann, Wiesław Szwast & Lidia Tendera - forthcoming - Journal of Symbolic Logic:1-30.
  13.  10
    Finite satisfiability for two‐variable, first‐order logic with one transitive relation is decidable.Ian Pratt-Hartmann - 2018 - Mathematical Logic Quarterly 64 (3):218-248.
    We consider two‐variable, first‐order logic in which a single distinguished predicate is required to be interpreted as a transitive relation. We show that the finite satisfiability problem for this logic is decidable in triply exponential non‐deterministic time. Complexity falls to doubly exponential non‐deterministic time if the transitive relation is constrained to be a partial order.
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  14.  2
    A two-variable fragment of English.Ian Pratt-Hartmann - 2003 - Journal of Logic, Language and Information 12 (1):13-45.
    Controlled languages are regimented fragments of natural languagedesigned to make the processing of natural language more efficient andreliable. This paper defines a controlled language, E2V, whose principalgrammatical resources include determiners, relative clauses, reflexivesand pronouns. We provide a formal syntax and semantics for E2V, in whichanaphoric ambiguities are resolved in a linguistically natural way. Weshow that the expressive power of E2V is equal to that of thetwo-variable fragment of first-order logic. It follows that the problemof determining the satisfiability of a set (...)
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  15.  16
    The two‐variable fragment with counting and equivalence.Ian Pratt-Hartmann - 2015 - Mathematical Logic Quarterly 61 (6):474-515.
    We consider the two‐variable fragment of first‐order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NExpTime‐complete. We further show that the corresponding problems for two‐variable first‐order logic with counting and two equivalences are both undecidable.
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  16.  11
    Spatial reasoning with RCC 8 and connectedness constraints in Euclidean spaces.Roman Kontchakov, Ian Pratt-Hartmann & Michael Zakharyaschev - 2014 - Artificial Intelligence 217 (C):43-75.
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  17.  16
    Topology, connectedness, and modal logic.Roman Kontchakov, Ian Pratt-Hartmann, Frank Wolter & Michael Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 151-176.
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  18.  9
    Topology, connectedness, and modal logic.Roman Kontchakov, Ian Pratt-Hartmann, Frank Wolter & Michael Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 151-176.
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  19.  8
    Elementary polyhedral mereotopology.Ian Pratt-Hartmann & Dominik Schoop - 2002 - Journal of Philosophical Logic 31 (5):469-498.
    A region-based model of physical space is one in which the primitive spatial entities are regions, rather than points, and in which the primitive spatial relations take regions, rather than points, as their relata. Historically, the most intensively investigated region-based models are those whose primitive relations are topological in character; and the study of the topology of physical space from a region-based perspective has come to be called mereotopology. This paper concentrates on a mereotopological formalism originally introduced by Whitehead, which (...)
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  20.  3
    Editors' Preface.Nissim Francez & Ian Pratt-Hartmann - 2012 - Studia Logica 100 (4):663-665.
  21.  31
    The fluted fragment with transitive relations.Ian Pratt-Hartmann & Lidia Tendera - 2022 - Annals of Pure and Applied Logic 173 (1):103042.
    The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, (...)
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  22.  2
    Adding Guarded Constructions to the Syllogistic.Ian Pratt-Hartmann - 2021 - In Judit Madarász & Gergely Székely (eds.), Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic. Springer. pp. 139-163.
    The relational syllogistic extends the classical syllogistic by allowing predicate phrases of the forms “rs every q”, “rs some q” and their negations, where q is a common noun and r a transitive verb. It is known that both the classical and relational syllogistic admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete. In this article, we extend the classical and relational syllogistic by allowing ‘guarded’ predicate phrases of the form “rs onlyqs”, and their (...)
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  23.  8
    Conditionalization and total knowledge.Ian Pratt-Hartmann - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):247-266.
    This paper employs epistemic logic to investigate the philosophical foundations of Bayesian updating in belief revision. By Bayesian updating, we understand the tenet that an agent's degrees of belief—assumed to be encoded as a probability distribution—should be revised by conditionalization on the agent's total knowledge up to that time. A familiar argument, based on the construction of a diachronic Dutch book, purports to show that Bayesian updating is the only rational belief-revision policy. We investigate the conditions under which the premises (...)
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  24.  6
    Fragments of first-order logic.Ian Pratt-Hartmann - 2023 - Oxford: Oxford University Press.
    A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are algorithmically solvable (...)
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  25. Semantic complexity in natural language.Ian Pratt-Hartmann - 1996 - In Shalom Lappin & Chris Fox (eds.), Handbook of Contemporary Semantic Theory. Hoboken: Wiley-Blackwell.
     
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  26.  6
    Advances in Modal Logic, Volume 5: Papers From the Fifth Aiml Conference, Held in Manchester, 9-11 September 2004.Renate A. Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.) - 2005 - London, England: King's College Publications.
    Modal logic is one of the most widely applied logical formalisms. Systems of modal logic are being used in many disciplines, ranging from artificial intelligence, computer science, mathematics, formal grammar and semantics to philosophy. This volume presents substantial recent advances in the relational and the algorithmic treatment of modal logics. It contains papers from the fifth conference on "Advances in Modal logic," held in Manchester (UK) in September 2004. Written by leading experts in the field, the present book is indispensable (...)
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  27.  18
    Joseph Y. Halpern. Reasoning about Uncertainty. MIT Press Cambridge, MA, 2003, xiv + 483 pp. [REVIEW]Ian Pratt-Hartmann - 2004 - Bulletin of Symbolic Logic 10 (3):427-429.