The taming of recurrences in computability logic through cirquent calculus, Part II
نویسنده
چکیده
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ¬, parallel conjunction ∧, parallel disjunction ∨, branching recurrence ◦ | , and branching corecurrence ◦| . The article is published in two parts, with (the previous) Part I containing preliminaries and a soundness proof, and (the present) Part II containing a completeness proof. MSC: primary: 03B47; secondary: 03B70; 68Q10; 68T27; 68T15.
منابع مشابه
Mathematical Logic The taming of recurrences in computability logic through cirquent calculus, Part II
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ¬, parallel conjunction ∧, parallel disjunction ∨, branching recurrence ◦| , and branching corecurrence ◦| . The article is published in two parts, with (the previous) Part I containing prelimin...
متن کاملMathematical Logic The taming of recurrences in computability logic through cirquent calculus, Part I
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ¬, parallel conjunction ∧, parallel disjunction ∨, branching recurrence ◦| , and branching corecurrence ◦| . The article is published in two parts, with (the present) Part I containing prelimina...
متن کاملThe taming of recurrences in computability logic through cirquent calculus, Part I
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ¬, parallel conjunction ∧, parallel disjunction ∨, branching recurrence ◦ | , and branching corecurrence ◦| . The article is published in two parts, with (the present) Part I containing prelimin...
متن کاملThe parallel versus branching recurrences in computability logic
This paper shows that the basic logic induced by the parallel recurrence ∧ | of Computability Logic (i.e., the one in the signature {¬,∧,∨,∧ | ,| }) is a proper superset of the basic logic induced by the branching recurrence ◦ | (i.e., the one in the signature {¬,∧,∨, ◦ | , ◦| }). The latter is known to be precisely captured by the cirquent calculus system CL15, conjectured by Japaridze to rema...
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Computability logic is a formal theory of computability. The earlier article “Introduction to cirquent calculus and abstract resource semantics” by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic. The present article extends that result to the more expressive cirquent calculus system CL6, which is a conservative extension of both CL5 and classical p...
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ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 52 شماره
صفحات -
تاریخ انتشار 2013