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Ian Pratt-Hartmann [14]Ian E. Pratt-Hartmann [1]
  1. Ian Pratt-Hartmann (2013). The Syllogistic with Unity. 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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  2. Nissim Francez & Ian Pratt-Hartmann (2012). Editors' Preface. Studia Logica 100 (4):663-665.
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  3. Ian Pratt-Hartmann (2011). The Hamiltonian Syllogistic. 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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  4. Ian Pratt-hartmann & Lawrence S. Moss (2009). Logics for the Relational Syllogistic. 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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  5. Ian Pratt-Hartmann (2008). On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics. 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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  6. Ian Pratt-Hartmann (2008). Conditionalization and Total Knowledge. Journal of Applied Non-Classical Logics 18 (2-3):247-266.
  7. Marco Aiello, Ian E. Pratt-Hartmann & Johan van Benthem (eds.) (2007). Handbook of Spatial Logics. Springer-Verlag.
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  8. Ian Pratt-Hartmann & Allan Third (2006). More Fragments of Language. 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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  9. Ian Pratt-Hartmann (2005). Complexity of the Two-Variable Fragment with Counting Quantifiers. 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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  10. J. Halpern & Ian Pratt-Hartmann (2004). REVIEWS-Reasoning About Uncertainty. Bulletin of Symbolic Logic 10 (3):427-429.
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  11. Ian Pratt-Hartmann (2004). Fragments of Language. 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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  12. Ian Pratt-Hartmann (2004). Halpern Joseph Y.. Reasoning About Uncertainty. MIT Press Cambridge, MA, 2003, Xiv+ 483 Pp. [REVIEW] Bulletin of Symbolic Logic 10 (3):427-429.
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  13. Ian Pratt-Hartmann (2003). A Two-Variable Fragment of English. 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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  14. Ian Pratt-Hartmann (2002). A Topological Constraint Language with Component Counting. Journal of Applied Non-Classical Logics 12 (3-4):441-467.
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  15. Ian Pratt-Hartmann & Dominik Schoop (2002). Elementary Polyhedral Mereotopology. 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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