相关论文: Information content in formal languages
The DL-Lite description logics allow for modeling domain knowledge on top of databases and for efficient reasoning. We focus on metric temporal extensions of DL-Lite_bool and its fragments, and study the complexity of satisfiability. In…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…
This paper deals with the problem of recognizability of functions l: Sigma* --> M that map words to values in the support set M of a monoid (M,.,1). These functions are called M-languages. M-languages are studied from the aspect of their…
Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an…
Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form $\exists y. \forall x. (\Box_x P(x,y) \supset\Diamond_y P(y,x))$. Like First order…
We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This…
We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet. More precisely, we prove that there is a bijective correspondence between varieties of languages recognized by orbit-finite nominal…
Logical depth and sophistication are two quantitative measures of the non-trivial organization of an object. Although apparently different, these measures have been proven equivalent, when the logical depth is renormalized by the busy…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes address the more general case when the coefficients are…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov and by Ben Yaacov, Doucha, Nies, and Tsankov, which are largely incompatible. With this we explicitly exhibit…
Scientific communication still mainly relies on natural language written in scientific papers, which makes the described knowledge very difficult to access with automatic means. We can therefore only make limited use of formal knowledge…
As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x \neq y\setminus z$, and $z =\{x\}$, where $x,y,z$ stand for variables ranging over the von…
Psycholinguistic studies of human word processing and lexical access provide ample evidence of the preferred nature of word-initial versus word-final segments, e.g., in terms of attention paid by listeners (greater) or the likelihood of…