Applications of scott's notion of consequence to the study of general binary intensional connectives and entailment

Dov M. Gabbay
<span title="">1973</span> <i title="Springer Nature America, Inc"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of Philosophical Logic</a> </i> &nbsp;
Synthese volume 92, D. Reidel, 1976. 321 pp, The main research thrust of this monograph is to present comprehensive methods for proving decidability and undecidability for modal and temporal systems. General theorems are proved on the one hand and new classification and semantical characterisations are given to many logics in order to show that they satisfy these general theorems. Counter examples are constructed to show the limitations of various methods. The book also lays the mathematical
more &raquo; ... conceptual foundations for non-classical logics. Semantical Investigations in Heyting's Intuitionistic Logic Synthese volume 148. D. Reidel, 1981. 300 pp, This monograph uses semantical methods to study intuitionistic and various neighbouring systems. It develops their mathematical model theory and finite model property and studies their proof theory and interpolation properties. It further applies the methods of book 1, to obtain decidability and undecidability results for intuitionistic algebraic theories. Both research monographs are partially based on, and extend, some of the related research papers. This paper outlines a general method for proving decidability and undecidability for non-classical logical systems. The method is based on Rabin's results on SwS and uses a variety of semantical and syntacticalinterpretations. It is the main, most powerful and most extensive method for solving the decision problem in the area of non-classical logics. Related papers which widely extend and develop the methods are 5This paper, which has had a strong following, proposes an answer to the question: what is a non-monotonic system? It gives axiomatic conditions on the notion of consequence relation, which characterises it as a non-monotonic logic. Further papers in this area are 53, 61 & 81, 95. This paper started the area now known as 'Axiomatic non-monotonic reasoning'. File: DovPapers/055/055-TFNMR.tex N-Prolog: An Extension of Prolog with Hypothetical Implications 2 Journal of Logic Programming, 2, 251-283, 1986. This paper is the first in a series in reformulating classical and non-classical logic in a goal directed way. It initiates the programme, continued in other papers of re-evaluating the notions of logic and proof theory in the light of applications of logic in Infomation Technology. Further papers are 54, 58, 59, 62, 65, 66, 79 and summarized in 87. Fibred Semantics for Feature Based Grammar Logic (with J. Dörre and E. König)
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