Caminada and Amgoud have argued that logic-based argumentation systems should satisfy the intuitive and natural principles of logical closure and consistency. Prakken has developed this idea further for a richer logic. A question arises naturally whether a general structure guaranteeing the logical closure and consistency properties could be identified that is common for all underlying logics. ...

In this paper we define and investigate basic logical closure properties of propositional proof systems such as closure of arbitrary proof systems under modus ponens or substitutions. As our main result we obtain a purely logical characterization of the degrees of schematic extensions of EF in terms of a simple combination of these properties. This result underlines the empirical evidence that ...

Patent search is an important information retrieval problem in scientific and business research. Semantic search would be a large improvement to current technologies, but requires some insight into the language of patents. In this article we test the fit of the language of patents to the sublanguage model, focussing on closure properties. The research presented here is relevant to the topic of ...

Recently in [Vij09, Corollary 3.7] the complexity class ModL has been shown to be closed under complement assuming NL = UL. In this note we continue to show many other closure properties of ModL which include

We classify the univariate functions that are relativizable closure properties of GapP, solving a problem posed by Hertrampf, Vollmer, and Wagner (Structures '95). We also give a simple proof of their classiication of univariate functions that are relativizable closure properties of #P.

Sublanguages are specialized genres of language associated with specific domains and document types. When sublanguages can be recognized and adequately characterized, they are useful for a variety of types of natural language processing applications. Although there are sublanguage studies related to languages other than English, all previous work on sublanguage recognition has focused on sublan...

Recently, the question has been raised whether the derivation tree languages of Minimalist grammars (MGs; [14, 16]) are closed under intersection with regular tree languages [4, 5]. Using a variation of a proof technique devised by Thatcher [17], I show that even though closure under intersection does not obtain, it holds for every MG and regular tree language that their intersection is identic...

Autostackability for finitely presented groups is a topological property of the Cayley graph combined with formal language theoretic restrictions, that implies solvability of the word problem. The class of autostackable groups is known to include all asynchronously automatic groups with respect to a prefix-closed normal form set, and all groups admitting finite complete rewriting systems. Altho...

Results from lattice theory have successfully been applied by several researchers, e.g. [1, 7, 9, 10], to reduce the complexity of verification of distributed computations. The set of all reachable states of a distributed computation forms a lattice under a certain partial order relation. A property is said to exhibit meet-closure if the set of reachable states satisfying it is closed under the...

In 1965 L. A Zadeh [11] introduced fuzzy sets as a generalization of ordinary sets. After that C. L. Chang [2] introduced fuzzy topology and that led to the discussion of various aspects of L-topology by many authors. The Čech closure spaces introduced by Čech E. [1] is a generalization of the topological spaces. The theory of fuzzy closure spaces has been established by Mashhour and Ghanim [4]...