27 research outputs found
On Problems Dual to Unification: The String-Rewriting Case
In this paper, we investigate problems which are dual to the unification
problem, namely the Fixed Point (FP) problem, Common Term (CT) problem and the
Common Equation (CE) problem for string rewriting systems. Our main motivation
is computing fixed points in systems, such as loop invariants in programming
languages. We show that the fixed point (FP) problem is reducible to the common
term problem. Our new results are: (i) the fixed point problem is undecidable
for finite convergent string rewriting systems whereas it is decidable in
polynomial time for finite, convergent and dwindling string rewriting systems,
(ii) the common term problem is undecidable for the class of dwindling string
rewriting systems, and (iii) for the class of finite, monadic and convergent
systems, the common equation problem is decidable in polynomial time but for
the class of dwindling string rewriting systems, common equation problem is
undecidable.Comment: 28 pages, 6 figures, will be submitted for LMCS journal. arXiv admin
note: substantial text overlap with arXiv:1706.0560
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book
Classification-based phrase structure grammar: an extended revised version of HPSG
This thesis is concerned with a presentation of Classification -based Phrase Structure
Grammar (or cPSG), a grammatical theory that has grown out of extensive revisions
of, and extensions to, HPSG. The fundamental difference between this theory and HPSG
concerns the central role that classification plays in the grammar: the grammar classifies
strings, according to their feature structure descriptions, as being of various types.
Apart from the role of classification, the theory bears a close resemblance to HPSG,
though it is by no means a direct translation, including numerous revisions and extensions.
A central goal in the development of the theory has been its computational
implementation, which is included in the thesis.The presentation may be divided into four parts. In the first, chapters 1 and 2, we
present the grammatical formalism within which the theory is stated. This consists of a
development of the notion of a classificatory system (chapter 1), and the incorporation
of hierarchality into that notion (chapter 2).The second part concerns syntactic issues. Chapter 3 revises the HPSG treatment of
specifiers, complements and adjuncts, incorporating ideas that specifiers and complements
should be distinguished and presenting a treatment of adjuncts whereby the
head is selected for by the adjunct. Chapter 4 presents several options for an account of
unbounded dependencies. The accounts are based loosely on that of GPSG, and a reconstruction
of GPSG's Foot Feature Principle is presented which does not involve a notion
of default. Chapter 5 discusses coordination, employing an extension of Rounds- Kasper
logic to allow a treatment of cross -categorial coordination.In the third part, chapters 6, 7 and 8, we turn to semantic issues. We begin (Chapter 6)
with a discussion of Situation Theory, the background semantic theory, attempting to
establish a precise and coherent version of the theory within which to work. Chapter 7
presents the bulk of the treatment of semantics, and can be seen as an extensive revision
of the HPSG treatment of semantics. The aim is to provide a semantic treatment which
is faithful to the version of Situation Theory presented in Chapter 6. Chapter 8 deals
with quantification, discussing the nature of quantification in Situation Theory before
presenting a treatment of quantification in CPSG. Some residual questions about the
semantics of coordinated noun phrases are also addressed in this chapter.The final part, Chapter 9, concerns the actual computational implementation of the
theory. A parsing algorithm based on hierarchical classification is presented, along with
four strategies that might be adopted given that algorithm. Also discussed are some
implementation details. A concluding chapter summarises the arguments of the thesis
and outlines some avenues for future research
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
Topics in Programming Languages, a Philosophical Analysis through the case of Prolog
[EN]Programming languages seldom find proper anchorage in philosophy of logic, language and science. is more, philosophy of language seems to be restricted to natural languages and linguistics, and even philosophy of logic is rarely framed into programming languages topics. The logic programming paradigm and Prolog are, thus, the most adequate paradigm and programming language to work on this subject, combining natural language processing and linguistics, logic programming and constriction methodology on both algorithms and procedures, on an overall philosophizing declarative status. Not only this, but the dimension of the Fifth Generation Computer system related to strong Al wherein Prolog took a major role. and its historical frame in the very crucial dialectic between procedural and declarative paradigms, structuralist and empiricist biases, serves, in exemplar form, to treat straight ahead philosophy of logic, language and science in the contemporaneous age as well.
In recounting Prolog's philosophical, mechanical and algorithmic harbingers, the opportunity is open to various routes. We herein shall exemplify some:
- the mechanical-computational background explored by Pascal, Leibniz, Boole, Jacquard, Babbage, Konrad Zuse, until reaching to the ACE (Alan Turing) and EDVAC (von Neumann), offering the backbone in computer architecture, and the work of Turing, Church, Gödel, Kleene, von Neumann, Shannon, and others on computability, in parallel lines, throughly studied in detail, permit us to interpret ahead the evolving realm of programming languages. The proper line from lambda-calculus, to the Algol-family, the declarative and procedural split with the C language and Prolog, and the ensuing branching and programming languages explosion and further delimitation, are thereupon inspected as to relate them with the proper syntax, semantics and philosophical élan of logic programming and Prolog
Combined decision procedures for nonlinear arithmetics, real and complex
We describe contributions to algorithmic proof techniques for deciding the satisfiability
of boolean combinations of many-variable nonlinear polynomial equations and
inequalities over the real and complex numbers.
In the first half, we present an abstract theory of Grobner basis construction algorithms
for algebraically closed fields of characteristic zero and use it to introduce
and prove the correctness of Grobner basis methods tailored to the needs of modern
satisfiability modulo theories (SMT) solvers. In the process, we use the technique of
proof orders to derive a generalisation of S-polynomial superfluousness in terms of
transfinite induction along an ordinal parameterised by a monomial order. We use this
generalisation to prove the abstract (“strategy-independent”) admissibility of a number
of superfluous S-polynomial criteria important for efficient basis construction. Finally,
we consider local notions of proof minimality for weak Nullstellensatz proofs and give
ideal-theoretic methods for computing complex “unsatisfiable cores” which contribute
to efficient SMT solving in the context of nonlinear complex arithmetic.
In the second half, we consider the problem of effectively combining a heterogeneous
collection of decision techniques for fragments of the existential theory of real
closed fields. We propose and investigate a number of novel combined decision methods
and implement them in our proof tool RAHD (Real Algebra in High Dimensions).
We build a hierarchy of increasingly powerful combined decision methods, culminating
in a generalisation of partial cylindrical algebraic decomposition (CAD) which we
call Abstract Partial CAD. This generalisation incorporates the use of arbitrary sound
but possibly incomplete proof procedures for the existential theory of real closed fields
as first-class functional parameters for “short-circuiting” expensive computations during
the lifting phase of CAD. Identifying these proof procedure parameters formally
with RAHD proof strategies, we implement the method in RAHD for the case of
full-dimensional cell decompositions and investigate its efficacy with respect to the
Brown-McCallum projection operator.
We end with some wishes for the future
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.