10 found
Order:
  1.  6
    Jaśkowski's Criterion and Three-Valued Paraconsistent Logics.Alexander S. Karpenko - 1999 - Logic and Logical Philosophy 7:81.
    A survey is given of three-valued paraconsistent propositionallogics connected with Jaśkowski’s criterion for constructing paraconsistentlogics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  2.  63
    The Classification of Propositional Calculi.Alexander S. Karpenko - 2000 - Studia Logica 66 (2):253-271.
    We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  3.  16
    A Maximal Lattice of Implicational Logics'.Alexander S. Karpenko - 1992 - Bulletin of the Section of Logic 27:29-32.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  25
    Sheffer's Stroke for Prime Numbers.Alexander S. Karpenko - 1994 - Bulletin of the Section of Logic 23 (3).
    Direct download  
     
    Export citation  
     
    Bookmark  
  5.  9
    Four-Valued Logics BD and DM4: Expansions.Alexander S. Karpenko - 2017 - Bulletin of the Section of Logic 46 (1/2).
    The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by matrices having the same underlying algebra, but with a different choice of designated values, i.e. with one designated value. In the preceding literature both approaches were developed independently. Moreover, we present the lattices of the functional expansions of DM4.
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  6.  41
    Characterization of Prime Numbers in Łukasiewicz's Logical Matrix.Alexander S. Karpenko - 1989 - Studia Logica 48 (4):465 - 478.
    In this paper we define n+1-valued matrix logic Kn+1 whose class of tautologies is non-empty iff n is a prime number. This result amounts to a new definition of a prime number. We prove that if n is prime, then the functional properties of Kn+1 are the same as those of ukasiewicz's n +1-valued matrix logic n+1. In an indirect way, the proof we provide reflects the complexity of the distribution of prime numbers in the natural series. Further, we introduce (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  7.  11
    Philosophical Problems of Foundations of Logic.Alexander S. Karpenko - 2014 - Studia Humana 3 (1):13-26.
    In the paper the following questions are discussed: What is logical consequence? What are logical constants? What is a logical system? What is logical pluralism? What is logic? In the conclusion, the main tendencies of development of modern logic are pointed out.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  8.  17
    1. Preliminaries.Alexander S. Karpenko - 1986 - Bulletin of the Section of Logic 15 (3):102-106.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  9.  9
    Algebraic Structure of the Truth-Values for Lω.Alexander S. Karpenko - 1988 - Bulletin of the Section of Logic 17 (3/4):127-133.
    This paper is an abstract of the report which was presented on the Polish-Soviet meeting on logic . It is shown that one can consider a lineary-ordered Heyting’s and Brouwer’s algebras as truth-values for Lukasiewicz’s infinite-valued logic’s Lω.
    Direct download  
     
    Export citation  
     
    Bookmark  
  10. Atomic and Molecular Paraconsistent Logics.Alexander S. Karpenko - 2002 - Logique Et Analyse 45 (178):31-37.
     
    Export citation  
     
    Bookmark