Translating often has the meaning of converting from one human language to another. However, in a broader sense, it means transforming message form communication another form. Logic is an important and ability translate natural into logic many different fields, which logical reasoning arguments are used. In legal field, for example, judges must reason facts presented conclusions. this paper, to...

The article includes schemes of defining by structural induction, and definitions and theorems related to: the set of variables which have free occurrences in a ZF-formula, the set of all valuations of variables in a model, the set of all valuations which satisfy a ZF-formula in a model, the satisfiability of a ZF-formula in a model by a valuation, the validity of a ZF-formula in a model, the a...

We study the decision problem for the language DGRA (directed graphs with reachability and acyclicity), a quantifier-free fragment of graph theory involving the notions of reachability and acyclicity. We prove that the language DGRA is decidable, and that its decidability problem is NP -complete. We do so by showing that the language enjoys a small model property : If a formula is satisfiable, ...

MAX-IND-SET def = {(G, k) : the largest independent set in G has size exactly k} . This language does not appear to be in NP: we can certify that some graph G has an independent set of size k, but how do we certify that this is the largest independent set in G? The language does not appear to be in coNP, either: although we could prove that (G, k) 6∈ MAX-IND-SET if G happened to have an indepen...

A Script Language in this paper is designed to transform the original data into the target data by the computing formula. The Script Language can be translated into the corresponding SQL Language, and the computation is finally implemented by the first type of dynamic SQL. The Script Language has the operations of insert, update, delete, union, intersect, and minus for the table in the database...

We present a truth-functional semantics for necessity-valued logics, based on the forcing technique. We interpret possibility distributions (which correspond to necessity measures) as informational states, and introduce a suitable language (basically, an extension of classical logic, similar to Pavelka’s language). Then we define the relation of “forcing” between an informational state and a fo...

Interactive software systems that are designed to offer proving and computing facilities at the same time face the problem of evaluation of formulae: In the situation of computing, a formula given to the system should be evaluated whereas in the situation of proving the formula should be kept unevaluated. Also, in the Theorema project we use the same language (Mathematica 3.0) as the working la...

In this paper we propose a layered framework for charging QoS-enhanced IP services with policy based configuration of its layers. As an example architecture we present our implementation Value Added IP Charging and Accounting Service (VIPCAS). We further concentrate on VIPCAS elements for policies and data exchange. As flexible data structure for exchange of accounting information, we propose t...

While neural network approaches are achieving breakthrough performance in the natural language related €elds, there have been few similar aŠempts at mathematical language related tasks. In this study, we explore the potential of applying neural representation techniques to Mathematical Information Retrieval (MIR) tasks. In more detail, we €rst brieƒy analyze the characteristic di‚erences betwee...

We present a novel coalgebraic logic for deterministic Mealy machines that is sound, complete and expressive w.r.t. bisimulation. Every finite Mealy machine corresponds to a finite formula in the language. For the converse, we give a compositional synthesis algorithm which transforms every formula into a finite Mealy machine whose behaviour is exactly the set of causal functions satisfying the ...