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The Finite Model Property For Various Fragments Of Linear Logic
, 1997
"... B stand for formulas. The connectives of propositional linear logic are: ffl the multiplicatives A & B, A\Omega B, ?, 1; ffl the additives A&B, A \Phi B, ?, 0; ffl the exponentials ?A, !A. Linear negation A ? is only given for positive atoms. It is extended to all formulas by A ?? = A and by ..."
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Cited by 25 (0 self)
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B stand for formulas. The connectives of propositional linear logic are: ffl the multiplicatives A & B, A\Omega B, ?, 1; ffl the additives A&B, A \Phi B, ?, 0; ffl the exponentials ?A, !A. Linear negation A ? is only given for positive atoms. It is extended to all formulas by A ?? = A and by (A & B) ? = A ?\Omega B ? ; ? ? = 1; (A &B) ? = A ? \Phi B ?
The Undecidability Of Second Order Linear Logic Without Exponentials
 Journal of Symbolic Logic
, 1995
"... . Recently, Lincoln, Scedrov and Shankar showed that the multiplicative fragment of second order intuitionistic linear logic is undecidable, using an encoding of second order intuitionistic logic. Their argument applies to the multiplicativeadditive fragment, but it does not work in the classical c ..."
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Cited by 12 (3 self)
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. Recently, Lincoln, Scedrov and Shankar showed that the multiplicative fragment of second order intuitionistic linear logic is undecidable, using an encoding of second order intuitionistic logic. Their argument applies to the multiplicativeadditive fragment, but it does not work in the classical case, because second order classical logic is decidable. Here we show that the multiplicativeadditive fragment of second order classical linear logic is also undecidable, using an encoding of twocounter machines originally due to Kanovich. The faithfulness of this encoding is proved by means of the phase semantics. In this paper, we write LL for the full propositional fragment of linear logic, MLL for the multiplicative fragment, MALL for the multiplicativeadditive fragment, and MELL for the multiplicativeexponential fragment. Similarly, we write ILL, IMLL, etc. for the fragments of intuitionistic linear logic, LL2, MLL2, etc. for the second order fragments of linear logic, and ILL2, IML...
Phase Semantics and Verification of Concurrent Constraint Programs
, 1998
"... The class CC of concurrent constraint programming languages and its nonmonotonic extension LCC based on linear constraint systems can be given a logical semantics in Girard's intuitionistic linear logic for a variety of observables. In this paper we settle basic completeness results and we show how ..."
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Cited by 11 (2 self)
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The class CC of concurrent constraint programming languages and its nonmonotonic extension LCC based on linear constraint systems can be given a logical semantics in Girard's intuitionistic linear logic for a variety of observables. In this paper we settle basic completeness results and we show how the phase semantics of linear logic can be used to provide simple and very concise "semantical" proofs of safety properties for CC or LCC programs.
Simulating Computations in Second Order NonCommutative Linear Logic (Preliminary Report)
, 1995
"... this paper we prove that the combination: "left and right implications ..."
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this paper we prove that the combination: "left and right implications
The Undecidability of Second Order Linear Affine Logic
, 1995
"... The quantiferfree propositional linear ane logic (i.e. linear logic with the weakening) is decidable. Recently, Lafont and Scedrov proved that multiplicative fragment of secondorder linear logic is undecidable. In this paper we show that the second order linear ane logic is undecidable too. At the ..."
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The quantiferfree propositional linear ane logic (i.e. linear logic with the weakening) is decidable. Recently, Lafont and Scedrov proved that multiplicative fragment of secondorder linear logic is undecidable. In this paper we show that the second order linear ane logic is undecidable too. At the same time it turns out that even its multiplicative fragment is undecidable. Moreover, we obtain the whole class of undecidability second order logics which lie between Lambek calculus (LC) and linear ane logic. The proof is based on an encoding twocounter Minsky machines in second order linear ane logic. The faithfulness of the encoding is proved by means of the phase semantic.
Decision Problems for SecondOrder Linear Logic
 Proceedings of the Tenth Annual IEEE Symposium on Logic in Computer Science
, 1995
"... Abstract. The decision problem is studied for fragments of secondorder linear logic without modalities. It is shown that the structural rules of contraction and weakening may be simulated by secondorder propositional quantifiers and the multiplicative connectives. Among the consequences are the un ..."
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Abstract. The decision problem is studied for fragments of secondorder linear logic without modalities. It is shown that the structural rules of contraction and weakening may be simulated by secondorder propositional quantifiers and the multiplicative connectives. Among the consequences are the undecidability of the intuitionistic secondorder fragment of propositional multiplicative linear logic and the undecidability of multiplicative linear logic with firstorder and secondorder quantifiers. 1 Introduction Much of the expressive power and plasticity of linear logic may be traced to the prohibition of structural rules of Contraction and to some extent Weakening [7, 9, 28, 25, 26]. These rules are reintroduced into linear logic in a controlled fashion by the logical rules for modalities (or: exponentials), which allow, for instance, intuitionistic implication or function type A ) B to be expressed as !A \GammaffiB. Without the use of modalities, however, any reintroduction of th...
Reasoning on Assembly Code using Linear Logic
, 2013
"... We present a logic for reasoning on assembly code. The logic is an extension of intuitionistic linear logic with greatest fixed points, pointer assertions for reasoning about the heap, and modalities for reasoning about program execution. One of the modality corresponds to the step relation of the s ..."
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We present a logic for reasoning on assembly code. The logic is an extension of intuitionistic linear logic with greatest fixed points, pointer assertions for reasoning about the heap, and modalities for reasoning about program execution. One of the modality corresponds to the step relation of the semantics of an assembly code interpreter. Safety is defined as the greatest fixed point of this modal operator. We can deal with first class code pointers, in a modular way, by defining an indexed model of the logic. 1.
Nondeterministic Phase Semantics and the Undecidability of Boolean BI
, 2011
"... We solve the open problem of the decidability of Boolean BI logic (BBI), which can be considered as the “core” of Separation and Spatial Logics. For this, we define a complete phase semantics suitable for BBI and characterize it as trivial phase semantics. We deduce an embedding between trivial phas ..."
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We solve the open problem of the decidability of Boolean BI logic (BBI), which can be considered as the “core” of Separation and Spatial Logics. For this, we define a complete phase semantics suitable for BBI and characterize it as trivial phase semantics. We deduce an embedding between trivial phase semantics for intuitionistic linear logic (ILL) and Kripke semantics for BBI. We single out the elementary fragment of ILL which is both undecidable and complete for trivial phase semantics. Thus, we obtain the undecidability of BBI.