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56
On the complexity of delp through game semantics
 Clausthal University
, 2006
"... Defeasible Logic Programming (DeLP) is a general argumentation based system for knowledge representation and reasoning. Its proof theory is based on a dialectical analysis where arguments for and against a literal interact in order to determine whether this literal is believed by a reasoning agen ..."
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Defeasible Logic Programming (DeLP) is a general argumentation based system for knowledge representation and reasoning. Its proof theory is based on a dialectical analysis where arguments for and against a literal interact in order to determine whether this literal is believed by a reasoning agent. The semantics GS is a declarative trivalued gamebased semantics for DeLP that is sound and complete for DeLP proof theory. Complexity theory is an important tool for comparing different formalism and for helping to improve implementations whenever it is possible. In this work we address the problem of studying the complexity of some important decision problems in DeLP. Thus, we characterize the relevant decision problems in the context of DeLP and GS, and we define data and combined complexity for DeLP. Since DeLP computes every argument from a set of defeasible rules, it is of central importance to analyze the complexity of two decision problems. The first one can be defined as “Is a set of defeasible rules an argument for a literal under a defeasible logic program?”. We prove that this problem is Pcomplete. The second decision problem is “Does there exist an argument for a literal under a defeasible logic program?”. We prove that this problem is in NP. Furthermore, we study data complexity of query answering in the context of DeLP. As far as we know, data complexity has not been introduced in the context of argumentation systems.
Symmetry and Interactivity in Programming
 Bulletin of Symbolic Logic
, 2001
"... We recall some of the early occurrences of the notions of interactivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics. ..."
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We recall some of the early occurrences of the notions of interactivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics.
Comparing Hierarchies of Types in Models of Linear Logic
, 2003
"... We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distri ..."
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We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distributive laws % : ! : ! M G ) G ! N commuting to the promotion rule. The key ingredient of the proof is a notion of backandforth translation between the hierarchies of types induced by M and N. We apply this result to compare (1) the qualitative and the quantitative hierarchies induced by the coherence (or hypercoherence) space model, (2) several paradigms of games semantics: errorfree vs. erroraware, alternated vs. nonalternated, backtracking vs. repetitive, uniform vs. nonuniform.
B.: A survey of semantic description frameworks for programming languages
 SIGPLAN Not
, 2004
"... Formal semantic description is significant for design, reasoning and standardization of programming languages, and it plays an important part in the optimization of the compiler. However, compared to the amount of effort that has been made to the research of various semantic frameworks over more tha ..."
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Formal semantic description is significant for design, reasoning and standardization of programming languages, and it plays an important part in the optimization of the compiler. However, compared to the amount of effort that has been made to the research of various semantic frameworks over more than forty years, their actual applications are definitely frustrating. This survey reviews the history of developments on semantic description frame works for programming languages. It also illustrates features and actual applications of the main frameworks (including operational, deno tational, axiomatic and hybrid semantics). In some practical aspects, such as comprehensibility, extensibility and applicability, the qualitative comparisons of these frameworks are given distinctly. It suggests that a more popular formal semantic description should behave more elegantly in readability, modularity, abstractness, comparability, reasonability, applicability and toolsupport.
A Practical Linear Time Algorithm for Trivial Automata Model Checking of HigherOrder Recursion Schemes
"... The model checking of higherorder recursion schemes has been actively studied and is now becoming a basis of higherorder program verification. We propose a new algorithm for trivial automata model checking of higherorder recursion schemes. To our knowledge, this is the first practical model che ..."
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The model checking of higherorder recursion schemes has been actively studied and is now becoming a basis of higherorder program verification. We propose a new algorithm for trivial automata model checking of higherorder recursion schemes. To our knowledge, this is the first practical model checking algorithm for recursion schemes that runs in time linear in the size of the higherorder recursion scheme, under the assumption that the size of trivial automata and the largest order and arity of functions are fixed. The previous linear time algorithm was impractical due to a huge constant factor, and the only practical previous algorithm suffers from the hyperexponential worstcase time complexity, under the same assumption. The new algorithm is remarkably simple, consisting of just two fixedpoint computations. We have implemented the algorithm and confirmed that it outperforms Kobayashi’s previous algorithm in a certain case.
The safe lambda calculus
 of Lecture Notes in Computer Science
, 2007
"... Abstract. Safety is a syntactic condition of higherorder grammars that constrains occurrences of variables in the production rules according to their typetheoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition ..."
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Abstract. Safety is a syntactic condition of higherorder grammars that constrains occurrences of variables in the production rules according to their typetheoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition to the setting of the simplytyped lambda calculus. In contrast to the original definition of safety, our calculus does not constrain types (to be homogeneous). We show that in the safe lambda calculus, there is no need to rename bound variables when performing substitution, as variable capture is guaranteed not to happen. We also propose an adequate notion of βreduction that preserves safety. In the same vein as Schwichtenberg’s 1976 characterization of the simplytyped lambda calculus, we show that the numeric functions representable in the safe lambda calculus are exactly the multivariate polynomials; thus conditional is not definable. We also give a characterization of representable word functions. We then study the complexity of deciding betaeta equality of two safe simplytyped terms and show that this problem is PSPACEhard. Finally we give a gamesemantic analysis of safety: We show that safe terms are denoted by Pincrementally justified strategies. Consequently pointers in the game semantics of safe λterms are only necessary from order 4 onwards.
On the ubiquity of certain total type structures
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2007
"... It is a fact of experience from the study of higher type computability that a wide range of approaches to defining a class of (hereditarily) total functionals over N leads in practice to a relatively small handful of distinct type structures. Among these are the type structure C of KleeneKreisel co ..."
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It is a fact of experience from the study of higher type computability that a wide range of approaches to defining a class of (hereditarily) total functionals over N leads in practice to a relatively small handful of distinct type structures. Among these are the type structure C of KleeneKreisel continuous functionals, its effective substructure C eff, and the type structure HEO of the hereditarily effective operations. However, the proofs of the relevant equivalences are often nontrivial, and it is not immediately clear why these particular type structures should arise so ubiquitously. In this paper we present some new results which go some way towards explaining this phenomenon. Our results show that a large class of extensional collapse constructions always give rise to C, C eff or HEO (as appropriate). We obtain versions of our results for both the “standard” and “modified” extensional collapse constructions. The proofs make essential use of a technique due to Normann. Many new results, as well as some previously known ones, can be obtained as instances of our theorems, but more importantly, the proofs apply uniformly to a whole family of constructions, and provide strong evidence that the above three type structures are highly canonical mathematical objects.
Games and Sequential Algorithms
, 2001
"... The relationship between HylandOngstyle games and BerryCurien sequential algorithms is investigated, with the object of describing semantic solutions to two problems  to characterise eectively the \minimal models" of the simplytyped calculus and the fully abstract model of PCF with co ..."
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The relationship between HylandOngstyle games and BerryCurien sequential algorithms is investigated, with the object of describing semantic solutions to two problems  to characterise eectively the \minimal models" of the simplytyped calculus and the fully abstract model of PCF with control operators  which are shown to be equivalent.