Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

Local Languages, the Succesor Method, and a Step Towards a General Methodology for the Inference of Regular Grammars

Abstract: A methodology is proposed for the inference of regular grammars from positive samples of their languages. It is mainly based on the generative mechanism associated with local languages, which allows us to obtain arbitrary regular languages by applying morphic operators to local languages. The actual inference procedure of this methodology consists of obtaining a local language associated with the given positive sample. This procedure, which is very simple, is always the same, regardless of the problem considered, while the task-dependent features that are desired for the inferred languages, are specified through the definition of certain task-appropriate symbol renaming functions (morphisms).

Logic Programming

Abstract: Logic programming emerged in the early 1970s from a convergence of work in the fields of automated theorem proving (q.v.), artificial intelligence (q.v.), and formal languages (q.v.).

Symbolic functions from neural computation

Abstract: Is thought computation over ideas? Turing, and many cognitive scientists since, have assumed so, and formulated computational systems in which meaningful concepts are encoded by symbols which are the objects of computation. Cognition has been carved into parts, each a function defined over such symbols. This paper reports on a research program aimed at computing these symbolic functions without computing over the symbols. Symbols are encoded as patterns of numerical activation over multiple abstract neurons, each neuron simultaneously contributing to the encoding of multiple symbols. Computation is carried out over the numerical activation values of such neurons, which individually have no conceptual meaning. This is massively parallel numerical computation operating within a continuous computational medium. The paper presents an axiomatic framework for such a computational account of cognition, including a number of formal results. Within the framework, a class of recursive symbolic functions can be computed. Formal languages defined by symbolic rewrite rules can also be specified, the subsymbolic computations producing symbolic outputs that simultaneously display central properties of both facets of human language: universal symbolic grammatical competence and statistical, imperfect performance.

Non-determinism in logic-based languages

Abstract: The use of non-determinism in logic-based languages is motivated using pragmatic and theoretical considerations. Non-deterministic database queries and updates occur naturally, and there exist non-deterministic implementations of various languages. It is shown that non-determinism resolves some difficulties concerning the expressive power of deterministic languages: there are non-deterministic languages expressing low complexity classes of queries/updates, whereas no such deterministic languages are known. Various mechanisms yielding non-determinism are reviewed. The focus is on two closely related families of non-deterministic languages. The first consists of extensions of Datalog with negations in bodies and/or heads of rules, with non-deterministic fixpoint semantics. The second consists of non-deterministic extensions of first-order logic and fixpoint logics, using thewitness operator. The expressive power of the languages is characterized. In particular, languages expressing exactly the (deterministic and non-deterministic) queries/updates computable in polynomial time are exhibited, whereas it is conjectured that no analogous deterministic language exists. The connection between non-deterministic languages and determinism is also explored. Several problems of practical interest are examined, such as checking (statically or dynamically) if a given program is deterministic, detecting coincidence of deterministic and non-deterministic semantics, and verifying termination for non-deterministic programs.

Non-Standard Semantics for Program Slicing

Abstract: In this paper we generalize the notion of compositional semantics to cope with transfinite reductions of a transition system. Standard denotational and predicate transformer semantics, even though compositional, provide inadequate models for some known program manipulation techniques. We are interested in the systematic design of extended compositional semantics, observing possible transfinite computations, i.e. computations that may occur after a given number of infinite loops. This generalization is necessary to deal with program manipulation techniques modifying the termination status of programs, such as program slicing. We include the transfinite generalization of semantics in the hierarchy developed in 1997 by P. Cousot, where semantics at different levels of abstraction are related with each other by abstract interpretation. We prove that a specular hierarchy of non-standard semantics modeling transfinite computations of programs can be specified in such a way that the standard hierarchy can be derived by abstract interpretation. We prove that non-standard transfinite denotational and predicate transformer semantics can be both systematically derived as solutions of simple abstract domain equations involving the basic operation of reduced power of abstract domains. This allows us to prove the optimality of these semantics, i.e. they are the most abstract semantics in the hierarchy which are compositional and observe respectively the terminating and initial states of transfinite computations, providing an adequate mathematical model for program manipulation.