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  1. Katarina Britz, Johannes Heidema & Ivan Varzinczak (2011). Constrained Consequence. Logica Universalis 5 (2):327-350.
    There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a (...)
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  2. Katarina Britz, Johannes Heidema & Willem Labuschagne (2009). Semantics for Dual Preferential Entailment. Journal of Philosophical Logic 38 (4):433 - 446.
    We introduce and explore the notion of duality for entailment relations induced by preference orderings on states. We discuss the relationship between these preferential entailment relations from the perspectives of Boolean algebra, inference rules, and modal axiomatisation. Interpreting the preference relations as accessibility relations establishes modular Gödel-Löb logic as a suitable modal framework for rational preferential reasoning.
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  3. Isabella C. Burger & Johannes Heidema (2005). For Better, for Worse: Comparative Orderings on States and Theories. Poznan Studies in the Philosophy of the Sciences and the Humanities 83 (1):459-488.
    In logic, including the designer logics of artificial intelligence, and in the philosophy of science, one is often concerned with qualitative, comparative orderings on the states of a system, or on theories expressing information about the system. States may be compared with respect to normality, or some preference criterium, or similarity to some given (set of) state(s). Theories may be compared with respect to logical power, or to truthlikeness, or to how well they capture certain information. We explain a number (...)
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  4. Willem A. Labuschagne & Johannes Heidema (2005). Natural and Artificial Cognition: On the Proper Place of Reason. South African Journal of Philosophy 24 (2):137-149.
    We explore the psychological foundations of Logic and Artificial Intelligence, touching on representation, categorisation, heuristics, consciousness, and emotion. Specifically, we challenge Dennett's view of the brain as a syntactic engine that is limited to processing symbols according to their structural properties. We show that cognitive psychology and neurobiology support a dual-process model in which one form of cognition is essentially semantical and differs in important ways from the operation of a syntactic engine. The dual-process model illuminates two important events in (...)
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  5. Emma Ruttkamp & Johannes Heidema (2005). Reviewing Reduction in a Preferential Model-Theoretic Context. [REVIEW] International Studies in the Philosophy of Science 19 (2):123 – 146.
    In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...)
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  6. Isabella C. Burger & Johannes Heidema (2002). Degrees of Abductive Boldness. In L. Magnani, N. J. Nersessian & C. Pizzi (eds.), Logical and Computational Aspects of Model-Based Reasoning. Kluwer Academic Publishers. 163--180.
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  7. Isabella Cornelia Burger & Johannes Heidema (2002). Merging Inference and Conjecture by Information. Synthese 131 (2):223 - 258.
    The intuitive notion of a binary relation on information-bearers, comparingthem with respect to their closeness to the available information, is oftenconstrued in terms of comparing their symmetric difference with, orcompositional similarity to, the available information. This happens forinstance in some treatments of verisimilitude. We expound an abstractmathematical rendering of the relevant data-dependent relation in theframework of Boolean algebras. For every element t of a Boolean algebra B we construct the t-modulated Boolean algebra Btin which the order relation represents `is at (...)
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  8. Thomas Meyer, Johannes Heidema, Willem Labuschagne & Louise Leenen (2002). Systematic Withdrawal. Journal of Philosophical Logic 31 (5):415-443.
    Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; (...)
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  9. Thomas Andreas Meyer, Willem Adrian Labuschagne & Johannes Heidema (2000). Infobase Change: A First Approximation. [REVIEW] Journal of Logic, Language and Information 9 (3):353-377.
    Generalisations of theory change involving operations on arbitrary sets ofwffs instead of on belief sets (i.e., sets closed under a consequencerelation), have become known as base change. In one view, a base should bethought of as providing more structure to its generated belief set, whichmeans that it can be employed to determine the theory contraction operationassociated with a base contraction operation. In this paper we follow suchan approach as the first step in defining infobase change. We think of an infobase (...)
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  10. Thomas Andreas Meyer, Willem Adrian Labuschagne & Johannes Heidema (2000). Refined Epistemic Entrenchment. Journal of Logic, Language and Information 9 (2):237-259.
    Epistemic entrenchment, as presented by Gärdenfors and Makinson (1988) and Gärdenfors (1988), is a formalisation of the intuition that, when forced to choose between two beliefs, an agent will giveup the less entrenched one. While their formalisation satisfactorilycaptures the intuitive notion of the entrenchment of beliefs in a number ofaspects, the requirement that all wffs be comparable has drawn criticismfrom various quarters. We define a set of refined versions of theirentrenchment orderings that are not subject to the same criticism, andinvestigate (...)
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  11. Isabella C. Burger & Johannes Heidema (1994). Comparing Theories by Their Positive and Negative Contents. British Journal for the Philosophy of Science 45 (2):605-630.
    relative to the actual world) of a propositional theory are defined. A theory is ‘closer to the truth’ the logically stronger its positive content and the logically weaker its negative content. This proposal delivers the same verisimilar preordering of theories that has been defined by Brink and Heidema as a ‘power ordering’. The preordering may be collapsed to a partial ordering and then embedded into a complete distributive lattice. The preordering may also be refined to a partial ordering by employing (...)
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  12. Chris Brink & Johannes Heidema (1991). Verisimilitude by Power Relations: A Response to Oddie. British Journal for the Philosophy of Science 42 (1):101-104.
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  13. Johannes Heidema (1990). An Axiom Schema of Comprehension of Zermelo–Fraenkel–Skolem Set Theory. History and Philosophy of Logic 11 (1):59-65.
    Unrestricted use of the axiom schema of comprehension, ?to every mathematically (or set-theoretically) describable property there corresponds the set of all mathematical (or set-theoretical) objects having that property?, leads to contradiction. In set theories of the Zermelo?Fraenkel?Skolem (ZFS) style suitable instances of the comprehension schema are chosen ad hoc as axioms, e.g.axioms which guarantee the existence of unions, intersections, pairs, subsets, empty set, power sets and replacement sets. It is demonstrated that a uniform syntactic description may be given of acceptable (...)
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  14. Chris Brink & Johannes Heidema (1987). A Verisimilar Ordering of Theories Phrased in a Propositional Language. British Journal for the Philosophy of Science 38 (4):533-549.
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