9 found
See also
  1.  16
    Metalogical Decorations of Logical Diagrams.Lorenz Demey & Hans Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
    In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...)
    Direct download (2 more)  
    Export citation  
    Bookmark   10 citations  
  2.  25
    Logical Geometries and Information in the Square of Oppositions.Hans Smessaert & Lorenz Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
    The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...)
    Direct download (4 more)  
    Export citation  
    Bookmark   15 citations  
  3.  12
    Combinatorial Bitstring Semantics for Arbitrary Logical Fragments.Lorenz Demey & Hans Smessaert - 2018 - Journal of Philosophical Logic 47 (2):325-363.
    Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...)
    Direct download (2 more)  
    Export citation  
    Bookmark   7 citations  
  4.  58
    On the 3d Visualisation of Logical Relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.
    The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition, namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us to define the Aristotelian relations in Boolean terms (...)
    Direct download (4 more)  
    Export citation  
    Bookmark   20 citations  
  5.  22
    The Classical Aristotelian Hexagon Versus the Modern Duality Hexagon.Hans Smessaert - 2012 - Logica Universalis 6 (1-2):171-199.
    Peters and Westerståhl (Quantifiers in Language and Logic, 2006), and Westerståhl (New Perspectives on the Square of Opposition, 2011) draw a crucial distinction between the “classical” Aristotelian squares of opposition and the “modern” Duality squares of opposition. The classical square involves four opposition relations, whereas the modern one only involves three of them: the two horizontal connections are fundamentally distinct in the Aristotelian case (contrariety, CR vs. subcontrariety, SCR) but express the same Duality relation of internal negation (SNEG). Furthermore, the (...)
    Direct download (3 more)  
    Export citation  
    Bookmark   6 citations  
  6.  69
    Temporal Reasoning with Aspectual Adverbs.Hans Smessaert & Alice G. B. Ter Meulen - 2004 - Linguistics and Philosophy 27 (2):209-261.
    Validity of dynamic temporal reasoning is semantically characterized for English and Dutch aspectual adverbs in Discourse Representation Theory. This dynamic perspective determines how the content needs to be revised and what information is preserved across updates, when the order of premises is considered relevant. Resetting contextual parameters relies on modelling the basic aspectual polarity transitions and temporal reasoning extensionally. For intensional aspectual adverbials the speaker’s attitudes regarding past alternatives to and possible continuations of the current state come into play. Additional (...)
    Direct download (8 more)  
    Export citation  
    Bookmark   1 citation  
  7.  32
    Pronounced Inferences: A Study on Inferential Conditionals.Sara Verbrugge, Kristien Dieussaert, Walter Schaeken, Hans Smessaert & William Van Belle - 2007 - Thinking and Reasoning 13 (2):105 – 133.
    An experimental study is reported which investigates the differences in interpretation between content conditionals (of various pragmatic types) and inferential conditionals. In a content conditional, the antecedent represents a requirement for the consequent to become true. In an inferential conditional, the antecedent functions as a premise and the consequent as the inferred conclusion from that premise. The linguistic difference between content and inferential conditionals is often neglected in reasoning experiments. This turns out to be unjustified, since we adduced evidence on (...)
    Direct download (2 more)  
    Export citation  
    Bookmark   3 citations  
  8.  20
    Monotonicity Properties of Comparative Determiners.Hans Smessaert - 1996 - Linguistics and Philosophy 19 (3):295 - 336.
    This paper presents a generalization of the standard notions of left monotonicity (on the nominal argument of a determiner) and right monotonicity (on the VP argument of a determiner). Determiners such as “more than/at least as many as” or “fewer than/at most as many as”, which occur in so-called propositional comparison, are shown to be monotone with respect to two nominal arguments and two VP-arguments. In addition, it is argued that the standard Generalized Quantifier analysis of numerical determiners such as (...)
    Direct download (6 more)  
    Export citation  
    Bookmark   3 citations  
  9.  29
    On the Argumentative Strength of Indirect Inferential Conditionals.Sara Verbrugge & Hans Smessaert - 2010 - Argumentation 24 (3):337-362.
    Inferential or epistemic conditional sentences represent a blueprint of someone’s reasoning process from premise to conclusion. Declerck and Reed (2001) make a distinction between a direct and an indirect type. In the latter type the direction of reasoning goes backwards, from the blatant falsehood of the consequent to the falsehood of the antecedent. We first present a modal reinterpretation in terms of Argumentation Schemes of indirect inferential conditionals (IIC’s) in Declerck and Reed (2001). We furthermore argue for a distinction between (...)
    Direct download (5 more)  
    Export citation