LOGICS AND METALOGICS
June 25, 2018, Afternoon

Workshop at UNILOG'2018 organized by

Mihir Chakraborty
Jadavpur University, Kolkota, India

The focus of the workshop lies in emphasizing the fact that in the study of logics, there always takes place an interplay between items belonging to object level, meta-level and metameta-level. Making a clear distinction of levels is crucial in logics, particularly in those systems where non-classical views are incorporated in the object language by denying bi-valence and/or denying some classical laws of reasoning. Many-valued logics, fuzzy logics , theory of graded consequence, Similarity based reasoning are a few to name. We shall base greatly on the prescription proposed by Alonzo Church in his book Introduction to Mathematical Logic, vol.1. Princeton University Press, N.J., 1956.

One of our attempts would be to draw attention to the fact that logic-studies do not usually pay due attention in distinguishing levels, due to which there do arise misconceptions, and even mistakes. Carnap's remark after Tarski's lecture at Vienna Circle meeting in the year 1930 may be recalled: "Of special interest to me was his emphasis that certain concepts used in logical investigations e.g., consistency of axioms, the provability of theorems in a deductive system, and the like are to be expressed not in the language of the axioms (later called the object language), but in metamathematical language (later called meta-language)."

However, in recent times this issue is being raised by some researchers, and in some cases, though it has not been explicitly mentioned, researchers introduced different languages for different levels of a logic discourse. Below we mention a few such references:

  • Bacon, A.: Non-classical Metatheory for Non-classical Logics, Journal of Philosophical Logic 42, 335-355, 2012.
  • Chakraborty, M.K.: Graded consequence: further studies. Journal of Applied Non-Classical Logics. 5, 227–237 (1995).
  • Chakraborty, M.K., Basu, S.: Graded consequence and some meta-logical notions generalized. Fundamenta Informaticae. 32, 299–311 (1997).
  • Chakraborty, M.K., Dutta, S.: Graded consequence revisited. Fuzzy Sets and Systems. 161, 1885– 1905 (2010).
  • Dutta S., Chakraborty, M.K.: The role of metalanguage in graded logical approaches. Fuzzy Sets and Systems, 298, 238-250, 2016.
  • Malinowski, G.: Q-consequence operation, Reports on Mathematical Logic, Vol 24, 49-59, 1990.
  • Malinowski, G.: Inferential many-valuedness, In Wolenski, J. (ed), Philosophical Logic in Poland, Kluwer, Amsterdam, 75-84, 1994.
  • Marraud, H.: Razonamiento Approximado Y Grados De Consecuencia, Endoxa, Vol 10, 55-70, 1998.
  • M. David P.: A graded inference approach based on infinite-valued Lukasiewicz semantics, in Proceedings of The International Symposium on Multiple-Valued Logic, 2010.
  • M. David P.: A Consequence Relation for Graded Inference within the Frame of Infinite-valued Lukasiewicz Logic, Fundamenta Informaticae, Vol 123, 77-95, 2013.
  • Parikh, R.: The Problem of Vague Predicates. In: Cohen, R.S., Wartof-sky, M. (eds.) Language, Logic, and Method, pp. 241-261. D. Ridel Publishing Company (1983)
  • Pelta, C.: Wide sets, deep many-valuedness and sorites arguments. Mathware and Soft computing, 11:5-11, 2004.
  • She, Y., Ma, L.: On the rough consistency measures of logic theories and approximate reasoning in rough logic, International Journal of Approximate Reasoning, 55(1):486499, 2014.
  • Vetterlein, T., Esteva, F., Godo, L.: Logics for Approximate Entail-ment in ordered universes of discourse, Int. J. Approx Reasoning, 71:50-63, 2016.

    Call for papers

    Relevant topics include (but are not restricted to):

    • the importance and essentiality of making level-distinction in logic
    • focusing current researches maintaining this distinction
    • scrutinizing logics that ignore this distinction
    • the ongoing debate on this issue

    Contributed talks should not exceed a duration of 30 minutes including discussion. A one-page abstract should be sent via email before December 1st, 2017 to: mihirc4@gmail.com

    		• .      .

     SCHEDULE 

    Keynote Speaker

    Soma Dutta
    Vistula University, Warsaw, Poland
    “Importance of distinction of levels in a logical discourse: an investigation from the perspective of a theory of graded consequence”


    Rohit Parikh
    CUNY, USA
    “Formalizing Umwelts”

    Invited and Contributing Speakers

    Walter Carnielli and Mamede Lima-Marques, Centre for Logic, Epistemology and the History of Science,Department of Philosophy, State University of Campinas, Brazil and University of Brasilia, Brazil, “Society semantics and meta-levels of many-valued logic”

    Carlos Pelta, Department of Basic Psychology II (Cognitive Processes), Complutense University of Madrid, Spain, “Partiality, Ignorance and Logical Consequence in L3”

    Graham Priest, Graduate Center, City University of New York, USA, “Dialetheic Validity”

    Jolly Thomas, International Institute of Information Technology, Hyderabad, India, “Formalizing Ontological Disputes of the Systems in Metaphysics by Augmenting First Order Quantificational Logic: A Meta-logical Inquiry”

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