| S. Demri and R. Gore. Tractable transformations from modal provability logics into first-order logic. In Automated Deduction---CADE-16, vol. 1632 of LNAI, pp. 16--30. Springer, 1999. |
....into the translation of a formula, or eliminating a relation with special properties by internalisation, is of course not new. Often, reductions between logics can be seen to use this principle. For example, De Giacomo [1] embedded CPDL into PDL by using an axiomatic encoding. Demri and Gore [5] embed the provability logics G and Grz into GF . Both are second order modal logics. This shows that with the axiomatic translation it is possible to get a first order translation of second order modal logics. De Giacomo s encoding of converse in PDL uses instances of schemata defined over ....
S. Demri and R. Gore. Tractable transformations from modal provability logics into first-order logic. In Automated Deduction -- CADE-16, vol. 1632 of LNAI, pp. 16--30. Springer, 1999.
....their soundness and completeness. In Section 4, we give necessary and su#cient conditions to establish that the display calculi admit a (limited) cut elimination theorem. Section 5 contains a similar analysis for traditional sequent style calculi. This paper is an extended and corrected version of [DG99b]. 2 Provability Logics Given a set PRP = 1 , p 2 , of atomic formulae, the formulae # FML are inductively defined as follows for p i PRP: # : # # p i # 2#. Standard abbreviations include 3: for instance, 3# 2#. An occurrence of the subformula # ....
S. Demri and R. Gore. Tractable transformations from modal provability logics into first-order logic. In H. Ganzinger, editor, CADE'99, pages 16--30. volume 1632 of Lecture Notes in Artificial Intelligence, Springer-Verlag, 1999.
....and show their soundness and completeness. In Section 4, we give necessary and sufficient conditions to establish that the display calculi admit a (limited) cut elimination theorem. Section 5 contains a similar analysis for traditional sequent style calculi. This paper is an extended version of [DG99d]. 2 2 Provability Logics Given a set For 0 = fp 1 ; p 2 ; g of atomic formulae, the formulae OE 2 For are inductively defined as follows for p i 2 For 0 : OE : j j p i j OE 1 OE 2 j OE 1 OE 2 j :OE j OE 1 ) OE 2 j 2OE Standard abbreviations include , 3: for instance, 3OE def = ....
S. Demri and R. Gor'e. Tractable transformations from modal provability logics into first-order logic. In H. Ganzinger, editor, CADE'99. LNAI 1632:16-30, Springer-Verlag, 1999.
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S. Demri and R. Gore. Tractable transformations from modal provability logics into first-order logic. In Automated Deduction---CADE-16, vol. 1632 of LNAI, pp. 16--30. Springer, 1999.
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