Theoretical Computer Science
Bounded linear logic: a modular approach to polynomial-time computability
Theoretical Computer Science
A decision procedure revisited: notes on direct logic, linear logic and its implementation
Theoretical Computer Science
A Predicate Calculus with Control of Derivations
CSL '89 Proceedings of the 3rd Workshop on Computer Science Logic
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Decidability of Linear Affine Logic
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Possible worlds and resources: the semantics of BI
Theoretical Computer Science - Mathematical foundations of programming semantics
Soft linear logic and polynomial time
Theoretical Computer Science - Implicit computational complexity
Combining Soft Linear Logic and Spatio-temporal Operators
Journal of Logic and Computation
A decidable first-order logic for medical reasoning
KES'11 Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part II
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It is known that Girard's linear logics can elegantly represent the concept of "resource consumption". The linear exponential operator ! in linear logics can express a specific infinitely reusable resource (i.e., it is reusable not only for any number, but also many times). It is also known that the propositional intuitionistic linear logic with ! and the first-order intuitionistic linear logic without ! (called here ILL) are undecidable and decidable, respectively. In this paper, a new decidable first-order intuitionistic linear logic, called the resource-indexed linear logic RL[l], is introduced by extending and generalizing ILL. The logic RL[l] has an l-bounded exponential operator !l, and this operator can express a specific finitely usable resource (i.e., it is usable in any positive number less than l+ 1, but only once). The embedding theorem of RL[l] into ILL is proved, and by using this theorem, the cut-elimination and decidability theorems for RL[l] are shown.