Standard Formal Language Research Articles

Temporal Truth and Bivalence: an Anachronistic Formal Approach to Aristotle’s De Interpretatione 9

Regarding the famous Sea Battle Argument, which Aristotle presents in De Interpretatione 9, there has never been a general agreement not only about its correctness but also, and mainly, about what the argument really is. According to the most natural reading of the chapter, the argument appeals to a temporal concept of truth and concludes that not every statement is always either true or false. However, many of Aristotle’s followers and commentators have not adopted this reading. I believe that it has faced so much resistance for reasons of hermeneutic charity: denying the law of universal bivalence seems to be overly disruptive to logical orthodoxy – the kind of logical orthodoxy represented by what we now call classical propositional logic, much of which Aristotle clearly supports in many texts. I intend to show that the logical-semantic theses that the traditional reading finds in De Interpretatione 9 are much more conservative than they may seem to be at first glance. First, I will show that they complement, and do not contradict in any way, the orthodox definitions of the concepts of truth and statement that Aristotle advances in other texts. Second, by resorting in an anachronistic vein to concepts and methods peculiar to contemporary logic, I will show that a trivalent modal semantics conforming to those theses can be built for a standard formal language of the classical propositional calculus. It is remarkable that reasonable concepts of logical truth and logical consequence that may be defined on the basis of this trivalent modal semantics are coextensive with their orthodox counterparts, the concepts of tautology and tautological consequence of classical bivalent and extensional semantics.

Pāṇini's Grammar and Modern Computation

Pāṇini's fourth (?) century BC Sanskrit grammar uses rewrite rules utilizing an explicit formal language defined through a semi-formal metalanguage. The grammar is generative, meaning that it is capable of expressing a potential infinity of well-formed Sanskrit sentences starting from a finite symbolic inventory. The grammar's operational rules involve extensive use of auxiliary markers, in the form of Sanskrit phonemes, to control grammatical derivations. Pāṇini's rules often utilize a generic context-sensitive format to identify terms used in replacement, modification or deletion operations. The context-sensitive rule format is itself defined using Pāṇini's more general method of auxiliary markers, the latter used to define many dozens of linguistic categories and rules controlling derivations of Sanskrit sentences through the manipulation of ‘non-terminal’ and ‘terminal’ symbols. This technique for controlling formal derivations was rediscovered by Emil Post in the 1920s and later shown by him to be capable of representing universal computation. The same implicit computational strength of Pāṇini's formalism follows as a consequence: while Pāṇini's Sanskrit grammar is computationally limited, the metalanguage through which his formalism is defined can be directly used to define any rule-based system by mimicking standard formal language definitions as an extension of the grammatical system proper. Pāṇini's formal achievement is historically distinctive, as derivations of grammatically correct, spoken Sanskrit, are designed for oral recitation, with the grammar itself constructed as an organic extension of the spoken object language. Pāṇini's formulation of what amounts to an orally realized symbolic calculus stands in contrast to the implicit inscriptional methods of contemporary formalisms, such as Gottlob Frege's appropriately named Begriffsschrift and the early computing paradigms of Post and Alan Turing. Nonetheless, contemporary views on the cognitive status of phonemic recognition and historical writing systems support the conjecture that, in spite of Pāṇini's rigorous oral formulation, construction of the grammar almost surely relied on alphabetic writing.

Prefixes, suffixes and substrings in a multilanguage: A perspective

In this paper, prefix, suffix and substring relations are described in a Multilanguage. It is shown that prefix and suffix relations give rise to a relational structure of a linear multiset order, and substring relations determine only a partial multiset order. The distinctive features of these relations in multilanguage vs. standard formal language are identified by using their graphical and Hasse diagram representations. Finally, certain monoids of these relations and their homomorphisms are described. Mathematics Subject Classification: 68Q45, 94A45, 03E02

Splicing in abstract families of languages

We show that the iterated splicing operation determined by a regular H scheme (with some necessary restrictions) preserves membership in any full abstract family of languages. This involves translation of an H scheme into two alternative forms. The first form, which is closely related to the underlying biochemical operations, uses cutting and pasting rather than splicing. The second form uses matrices of languages, and in this formulation the splicing operation is translated into standard formal language operations (concatenation and quotient). Moreover, in the matrix formulation the splicing language itself may be expressed in terms of standard formal language operations, and this provides an algorithm for calculating the splicing language. As an application we use the cutting and pasting approach to extend the closure result to circular strings.

SDL-TRAN—An interactive generator for formal description language SDL

SDL (Specification and Description Language) is an international standard formal description language which has been widely used for the specification and description of communication systems. SDL is based on the concept of the state oriented description technique—FSM (Finite State Machine). This paper reports an interactive generator for SDL, named SDL-TRAN, which can automatically translate FSM expression into SDL description. Except for its automatic translation part, SDL-TRAN includes an user-friendly graphical editor which is used to get the other part of SDL description which cannot be automatically translated.

An algorithm for speculative parallel execution of rendezvous-synchronized simulation

This paper presents an approach for speculative parallel execution of rendezvous-synchronized simulations. Rendezvous-synchronized simulation is based on the notions of processes and gates and on the rendezvous mechanism defined in the basic process algebra of LOTOS—a standard formal specification language for temporal ordering [2] . Time is introduced via a mechanism similar to the delay behaviour annotation provided by the TOPO toolset [4-6] . The algorithm allows speculative gate activations. This increases the available parallelism while ensuring correct execution of the computation. The model is used to describe closed stochastic queueing network simulations. Analysis of their execution results suggests that the model makes available a promising degree of parallelism.

Semi-automatic test suite generation from Estelle

Overviews of the standard formal specification language Estelle and test suite specification language TTCN are provided. Steps involved in semi-automatic generation of TTCN test suites from Estelle are introduced. Details of TTCN test step generation from Estelle transitions are explained. Test cases are obtained from these test steps by way of ordering them using the control flow graph. The implementation of a software tool called TTCNGEN, which largely automates the methodology, is explained and examples are provided from the LAP-D protocol of the integrated services digital network. Related research is discussed, and various ideas are highlighted for future research.

Comparison of subtheories

Let ZF denote the Zermelo-Fraenkel set theory and ZFI the theory obtained from it by the addition of an axiom which asserts the existence of at least one inaccessible number. If ZF is consistent then ZFI contains number-theoretic theorems which are not theorems of ZF, e.g. the arithmetical sentence which asserts the consistency of ZF-Con(ZF). Mostowski [4] introduced a sentence of the theory of real numbers which can be proved in ZFI but cannot be proved in ZF. Let S1 and S2 be two theories such that the relation of Si to S2 is like that of ZFI to ZF. The present paper will show to what extent the subtheories of S1 contain more theorems than the corresponding subtheories of S2. We shall use the terminology of Tarski-Mostowski-Robinson [8].2 A set of symbols of the first order predicate calculus with the usual formation rules for terms and formulae, as laid out in [8, pp. 6-7], will be called a standard formal language. Each theory with standard formalization is formalized in a standard formal language. If R is a standard formal language and P an unary predicate (P need not be a symbol of R) we construct a new formal language R(P) by the relativization of quantifiers in R to P (see [8, p. 24]). If A is a sentence of R we denote by A (P) the sentence obtained from A by relativizing the quantifiers in it to P. Let Q be a theory with standard formalization. We define the notion of an interpretation of R in Q as in [8, pp. 20-21, 29]. This interpretation is obtained by a new theory with standard formalization Q(R) which is formalized in the language which consists of the symbols of both Q and R(P). The valid sentences of Q(R) are exactly those which are derivable from the set which consists of the valid sentences of Q and possible definitions of the nonlogical constants of R(P) in Q. Given a particular interpretation of R in Q we can define in the language R a theory with standard formalization Q/R (which may be called the theory induced by Q in R) by the following stipulation: A sentence A of R is valid in Q/R