Image schemas via finite-state methods structured category-theoretically
|
|
- Stuart O’Connor’
- 6 years ago
- Views:
Transcription
1 Objective predication Subjective predication Reconciliation Image schemas via finite-state methods structured category-theoretically Tim Fernando Bolzano, 22 August 2016, PROSECCO a recurring structure within our cognitive processes which establishes patterns of understanding and reasoning (Wikipedia) Ontological logs (ologs) Institutions D. Spivak J. Goguen 1 / 21 Predication Donald is in trouble. Chelsea has, as mother, Hillary. Aristotle subject predicate containment Frege/RDF triple subject predicate object Graph (directed multi) vertex edge vertex Automata state label state? source path goal Category domain morphism ;= codomain category functor category Spivak olog interpretation I Set.... Linguistic motivation: individual-, kind-, stage-level predication (G. Carlson)
2 Agenda 1 Objective predication - declarative (logical) - extensional: concept c as a set I (c), where I is a functor from an olog C to Set 2 Subjective predication - procedural (cognitive) - attributional: concept c traced by strings over Σ 3 Reconciliation - institutions (schemas =) trace(c) Σ Goal: justify & develop finite-state methods for containment, path,... (image schemas) via some category theory Objective predication Subjective predication Reconciliation 1 Objective predication 2 Subjective predication 3 Reconciliation 4 / 21
3 Types vs instances : ologs & functors (1) Sylvester is a cat. cat(sylvester) sylvester I (cat) (2) Lions are cats. lion cat I (lion) I(cat) (3) Pat lives in }{{} Cork. f : A B in C (olog/database schema) I : C Set for I (f ) : I (A) I (B) in Set Grothendieck construction {}}{ (pat, f, cork) : (A, pat) (B, cork) in I pat I (A) & I (f )(pat) = cork Triplestores & database schemas person lives-in pat cork ann rome place state cork ireland rome italy (pat,lives-in,cork), (cork, state, ireland),... in I Olog/category C as top row + I for remaining rows person lives-in place place state state plus C-identities A = A A pat I (person) (pat, = person, pat) in I cork I (place) (cork, = place, cork) in I... composition - (pat, lives-in;state, ireland) in I
4 Predicates as transition labels, not morphisms Sylvester is a cat sylv I (cat) Lions are cats (sylv, = cat, sylv) in I I (lion) I (cat) Given I : C Set, - the RDF triple (a, f, b) is determined by (a, f ) with label f for transitions b = I (f )(a) a f I (f )(a) from a to I (f )(a) - I (A) I (B) can be encoded as (A, in(b)) with label in(b) for transitions A in(b) B from A to B. Objective predication Subjective predication Reconciliation 1 Objective predication 2 Subjective predication 3 Reconciliation 8 / 21
5 Traces q α q as (q, α, q ), where Q Σ Q For q 0 Q, let trace(q 0 ) := n 0{α 1 α n Σ n ( q 1 q n Q n ) α q i i 1 qi for 1 i n}. is deterministic if for all α Σ and q Q, there is at most one q s.t. q α q. Fact. If is deterministic, then trace equivalence q q trace(q) = trace(q ) is well-suited to (bisimulation equivalence). Brzozowski derivatives & finite-state matters For deterministic and q α q, trace(q ) = trace(q) α where For s = α 1 α n, L α = {s αs L} L s := {s ss L} L ɛ = L = {s ɛ L s } α s L L 1 α ɛ 2 Lα1 Lα1 α 2 αn L α1 α n = L s and ɛ L s. Myhill-Nerode L is regular {L s s Σ } is finite L s = L s ( w Σ ) (sw L s w L)
6 Q(Σ): composition as typed concatenation Always ɛ trace(q) and whenever sα trace(q), s trace(q). A Σ-state is a non-empty language L Σ that is prefix-closed sα L s L A Q(Σ)-morphism is a pair (L, s) of a Σ-state L and an s L with identities (L, ɛ) labeled by ɛ. dom(l, s) := L cod(l, s) := L s (L, s) ; (L s, s ) := (L, ss ) A B as A in(b) B allows trace(b) trace(a) (contra (L, ɛ)) but should we not expect L in(b) L? Labeled transitions from C I Set Yes, for built from I and on C A f B in C a f I (f )(a) a I (A) A, B C I (A) I (B) A in[b] B Are there enough labels for trace(pat) trace(ann)? Brute force differentiation via labels = a A C a = a a a I (A) Cognitive processes may pick up only some of these transitions. Connect instances and types by A C a in[a] A a I (A) A f B in C A f B raising the question L in(a) L (also for L = trace(a))?
7 Non-extensionality & non-monotonicity (a) Cats are widespread. (Carlson kind-level predication) Sylvester is widespread?? (b) Birds fly. Penguins are birds that don t. (Defaults...) Tweety is a penguin. (Penguin principle... DATR) Not only may types be more than sets of their instances, these instances may vary with time. (c) Sylvester was hungry this morning. (C stage-level) (d) Pat moved from Belfast to Cork in (events) Vary not only extension I : C Set described (change/events) but also granularity Σ (Vendler classes; Fernando 2016). Partiality: presheaves Fix a large set Θ of labels, with fragments in Fin(Θ) := {Σ Θ Σ is finite} Contravariant functor Q : Fin(Θ) op Cat for Σ Σ Fin(Θ), Q(Σ, Σ) : Q(Σ ) Q(Σ) L L Σ (L, s) (L Σ, s Σ ) where s Σ is the longest prefix of s in Σ. Morphisms in an olog vs Q(Σ): free monoid of strings (L, s) ; (L s, s ) := (L, ss ) Time as change: stutter-free strings from block compression bc( rain rain rain rain,sun sun sun ) = rain rain,sun sun (Fernando 2016)
8 Objective predication Subjective predication Reconciliation 1 Objective predication 2 Subjective predication 3 Reconciliation 15 / 21 Back to image schema (broadly) olog a { recurring }} structure { within our cognitive processes which establishes patterns of understanding and reasoning }{{} M = S ϕ Institution (Goguen): = as a schema instantiatied by a signature S relating S -models M and S -sentences ϕ Example 1. S is an olog C C-model is a functor I : C Set C-sentence is a path equation (commuting diagram) A f 1 f n g 1 g m B = A B Example 2. S is a finite alphabet Σ Σ-model is a Σ-state L Σ-sentence from Hennessy-Milner logic L = Σ α ϕ iff α L and L α = Σ ϕ
9 Three functors F : A Cat for F f Given A B in A, a F (A) and b F (B) (f,x) x (A, a) (B, b) in F F (f )(a) b in F (B) (i) F = I : }{{} C Set with sets as discrete categories olog Sign (only morphisms are identities) I is a C-model (ii) (iii) F = Q : Fin(Θ) op Cat with Q(Σ)-composition as typed concatenation Sign from Q (L s and s ϕ; Fernando 2016a) F = Th : Sign Cat with Th(S ) pre-ordered Γ S Γ {M M = S ϕ} {M M = S ϕ} ϕ Γ ϕ Γ Lattice of theories (LOT, Sowa) & ologs Spivak & Kent 2012 In the Olog formalism, LOT is locally represented by the entailment preorders spec(g)... the entailment ordering defines paths to the more generalized ologs above and the more specialized ologs below. Sowa defines four ways for moving along paths from one olog to another: contraction, expansion, revision and analogy Olog specification/equation A f 1 is broken down by Q to f n g 1 g m B = A B L f1 f n = L g1 g m for all L s.t. L in(a) or in Hennessy-Milner (interpreted by traces) ( in(a) f 1 f n ϕ g 1 g m ϕ) ( in(a) g 1 g m ϕ f 1 f n ϕ)
10 A finite-state calculus L = α Θ αl α + o(l) where o(l) = { ɛ if ɛ L otherwise both Taylor s theorem & the mean value theorem in this theory (Conway 1971) Finite approximability hypothesis: finite subset of Θ will do open-ended signature: Σ Fin(Θ) (directed poset) Sign = Q (inverse limit) Identity as indiscernibility (Leibniz) wrt Σ: bounded granularity Σ-sentences from Hennessy-Milner, Monadic Second-Order Logic (Fernando 2015, 2016, 2016a) Predication on kinds & stages via strings Extension I changes along path reflecting - inheritance hierarchy (finite) tweety penguin bird ϕ ϕ ϕ inheritable/inertial ϕ - time (bounded granularity) Ed explained E S E S Ed explaining E V E E,V E Reichenbach tense aspect it rained E,R S R S E,R it has rained E R,S R,S E R projection E,R S R S...
11 Some references G. Carlson, A unified analysis of the English bare plural, Linguistics & Philosophy 1(3):413 58, J.H. Conway, Regular Algebra & Finite Machines T. Fernando, Two perspectives on change & institutions, 2015 ( FOfAI paper 2.pdf). T. Fernando, On regular languages over power sets, Journal of Language Modelling 4(1):29 56, T. Fernando, Types from frames as finite automata, Formal Grammar, Springer LNCS 9804, 2016a, pp J. Goguen & R. Burstall, Institutions: Abstract model theory for specifications & programming. J. ACM 39(1):95 146, D.I. Spivak & R.E. Kent, Ologs: A categorical framework for knowledge representation. PLoS ONE 7(1), D.I. Spivak, Category Theory for the Sciences. MIT Press, 2014.
Two perspectives on change & institutions
Two perspectives on change & institutions Tim Fernando Trinity College Dublin, Ireland Nicola Guarino 2014 - Ontological analysis as a search for truth makers - Episodes as truth makers for material relations
More informationPredication via Finite-State Methods
Predication via Finite-State Methods 1. Introduction: Less is More Tim Fernando ESSLLI 2017, Toulouse www.scss.tcd.ie/tim.fernando/fsm4sas Course themes: finite-state approximability bounded granularity
More informationPredication via Finite-State Methods
Predication via Finite-State Methods 4/5. Finite-state truthmaking Tim Fernando ESSLLI 2017, Toulouse Key phrases: events vs statives vs forces ceteris paribus: explicit vs derived pathfinding granularity
More informationIterated Galois connections in arithmetic and linguistics. J. Lambek, McGill University
1 Iterated Galois connections in arithmetic and linguistics J. Lambek, McGill University Abstract: Galois connections may be viewed as pairs of adjoint functors, specialized from categories to partially
More informationIntervals & events with & without points
Intervals & events with & without points Tim Fernando (Dublin, Ireland) Stockholm, 2018 James Allen: intervals as primitive There seems to be a strong intuition that, given an event, we can always turn
More informationMathematical Foundations for Conceptual Blending
Mathematical Foundations for Conceptual Blending Răzvan Diaconescu Simion Stoilow Institute of Mathematics of the Romanian Academy FROM 2017 Part I Conceptual Blending: from Fauconnier and Turner to Goguen
More informationDuality in Probabilistic Automata
Duality in Probabilistic Automata Chris Hundt Prakash Panangaden Joelle Pineau Doina Precup Gavin Seal McGill University MFPS May 2006 Genoa p.1/40 Overview We have discovered an - apparently - new kind
More informationA Weak Bisimulation for Weighted Automata
Weak Bisimulation for Weighted utomata Peter Kemper College of William and Mary Weighted utomata and Semirings here focus on commutative & idempotent semirings Weak Bisimulation Composition operators Congruence
More informationPrior and temporal sequences for natural language
Prior and temporal sequences for natural language Tim Fernando Trinity College Dublin, Ireland Tim.Fernando@tcd.ie In a widely quoted defense of logics of discrete time, Arthur Prior writes The usefulness
More informationLecture three: Automata and the algebra-coalgebra duality
Lecture three: Automata and the algebra-coalgebra duality Jan Rutten CWI Amsterdam & Radboud University Nijmegen IPM, Tehran - 13 January 2016 This lecture will explain two diagrams: 1 x c ε σ A r x X
More informationA Polynomial Time Algorithm for Parsing with the Bounded Order Lambek Calculus
A Polynomial Time Algorithm for Parsing with the Bounded Order Lambek Calculus Timothy A. D. Fowler Department of Computer Science University of Toronto 10 King s College Rd., Toronto, ON, M5S 3G4, Canada
More informationEntailments in finite-state temporality
Entailments in finite-state temporality Tim Fernando and Rowan Nairn Computer Science Department, Trinity College Dublin 1 Introduction The surge in use of finite-state methods ([10]) in computational
More informationFinite-state Machines: Theory and Applications
Finite-state Machines: Theory and Applications Unweighted Finite-state Automata Thomas Hanneforth Institut für Linguistik Universität Potsdam December 10, 2008 Thomas Hanneforth (Universität Potsdam) Finite-state
More informationCategory Theory. Categories. Definition.
Category Theory Category theory is a general mathematical theory of structures, systems of structures and relationships between systems of structures. It provides a unifying and economic mathematical modeling
More informationThe Class CAT of Locally Small Categories as a Functor-Free Framework for Foundations and Philosophy
The Class CAT of Locally Small Categories as a Functor-Free Framework for Foundations and Philosophy Vaughan Pratt Stanford University Logic Colloquium UC Berkeley April 27, 2018 Vaughan Pratt Stanford
More informationThe State Explosion Problem
The State Explosion Problem Martin Kot August 16, 2003 1 Introduction One from main approaches to checking correctness of a concurrent system are state space methods. They are suitable for automatic analysis
More informationCATEGORY THEORY. Cats have been around for 70 years. Eilenberg + Mac Lane =. Cats are about building bridges between different parts of maths.
CATEGORY THEORY PROFESSOR PETER JOHNSTONE Cats have been around for 70 years. Eilenberg + Mac Lane =. Cats are about building bridges between different parts of maths. Definition 1.1. A category C consists
More informationPeter Wood. Department of Computer Science and Information Systems Birkbeck, University of London Automata and Formal Languages
and and Department of Computer Science and Information Systems Birkbeck, University of London ptw@dcs.bbk.ac.uk Outline and Doing and analysing problems/languages computability/solvability/decidability
More informationACLT: Algebra, Categories, Logic in Topology - Grothendieck's generalized topological spaces (toposes)
ACLT: Algebra, Categories, Logic in Topology - Grothendieck's generalized topological spaces (toposes) Steve Vickers CS Theory Group Birmingham 2. Theories and models Categorical approach to many-sorted
More informationObtaining the syntactic monoid via duality
Radboud University Nijmegen MLNL Groningen May 19th, 2011 Formal languages An alphabet is a non-empty finite set of symbols. If Σ is an alphabet, then Σ denotes the set of all words over Σ. The set Σ forms
More informationLanguage-Processing Problems. Roland Backhouse DIMACS, 8th July, 2003
1 Language-Processing Problems Roland Backhouse DIMACS, 8th July, 2003 Introduction 2 Factors and the factor matrix were introduced by Conway (1971). He used them very effectively in, for example, constructing
More informationFully Lexicalized Pregroup Grammars
Fully Lexicalized Pregroup Grammars Annie Foret joint work with Denis Béchet Denis.Bechet@lina.univ-nantes.fr and foret@irisa.fr http://www.irisa.fr/prive/foret LINA Nantes University, FRANCE IRISA University
More informationWhat You Must Remember When Processing Data Words
What You Must Remember When Processing Data Words Michael Benedikt, Clemens Ley, and Gabriele Puppis Oxford University Computing Laboratory, Park Rd, Oxford OX13QD UK Abstract. We provide a Myhill-Nerode-like
More informationPropositional logic. First order logic. Alexander Clark. Autumn 2014
Propositional logic First order logic Alexander Clark Autumn 2014 Formal Logic Logical arguments are valid because of their form. Formal languages are devised to express exactly that relevant form and
More information1 More finite deterministic automata
CS 125 Section #6 Finite automata October 18, 2016 1 More finite deterministic automata Exercise. Consider the following game with two players: Repeatedly flip a coin. On heads, player 1 gets a point.
More informationTowards Efficient String Processing of Annotated Events
Towards Efficient String Processing of Annotated Events David Woods 1 Tim Fernando 2 Carl Vogel 2 1 ADAPT Centre Trinity College Dublin, Ireland 2 Computational Linguistics Group Trinity Centre for Computing
More informationCHAPTER 2 INTRODUCTION TO CLASSICAL PROPOSITIONAL LOGIC
CHAPTER 2 INTRODUCTION TO CLASSICAL PROPOSITIONAL LOGIC 1 Motivation and History The origins of the classical propositional logic, classical propositional calculus, as it was, and still often is called,
More informationOutline. CS21 Decidability and Tractability. Machine view of FA. Machine view of FA. Machine view of FA. Machine view of FA.
Outline CS21 Decidability and Tractability Lecture 5 January 16, 219 and Languages equivalence of NPDAs and CFGs non context-free languages January 16, 219 CS21 Lecture 5 1 January 16, 219 CS21 Lecture
More informationHalting and Equivalence of Program Schemes in Models of Arbitrary Theories
Halting and Equivalence of Program Schemes in Models of Arbitrary Theories Dexter Kozen Cornell University, Ithaca, New York 14853-7501, USA, kozen@cs.cornell.edu, http://www.cs.cornell.edu/~kozen In Honor
More information06 From Propositional to Predicate Logic
Martin Henz February 19, 2014 Generated on Wednesday 19 th February, 2014, 09:48 1 Syntax of Predicate Logic 2 3 4 5 6 Need for Richer Language Predicates Variables Functions 1 Syntax of Predicate Logic
More informationKnowledge representation DATA INFORMATION KNOWLEDGE WISDOM. Figure Relation ship between data, information knowledge and wisdom.
Knowledge representation Introduction Knowledge is the progression that starts with data which s limited utility. Data when processed become information, information when interpreted or evaluated becomes
More informationSri vidya college of engineering and technology
Unit I FINITE AUTOMATA 1. Define hypothesis. The formal proof can be using deductive proof and inductive proof. The deductive proof consists of sequence of statements given with logical reasoning in order
More information1. The Method of Coalgebra
1. The Method of Coalgebra Jan Rutten CWI Amsterdam & Radboud University Nijmegen IMS, Singapore - 15 September 2016 Overview of Lecture one 1. Category theory (where coalgebra comes from) 2. Algebras
More informationIntroduction to Temporal Logic. The purpose of temporal logics is to specify properties of dynamic systems. These can be either
Introduction to Temporal Logic The purpose of temporal logics is to specify properties of dynamic systems. These can be either Desired properites. Often liveness properties like In every infinite run action
More informationInterpolation in Logics with Constructors
Interpolation in Logics with Constructors Daniel Găină Japan Advanced Institute of Science and Technology School of Information Science Abstract We present a generic method for establishing the interpolation
More informationFinite Presentations of Pregroups and the Identity Problem
6 Finite Presentations of Pregroups and the Identity Problem Alexa H. Mater and James D. Fix Abstract We consider finitely generated pregroups, and describe how an appropriately defined rewrite relation
More informationComputational Models - Lecture 4
Computational Models - Lecture 4 Regular languages: The Myhill-Nerode Theorem Context-free Grammars Chomsky Normal Form Pumping Lemma for context free languages Non context-free languages: Examples Push
More information1 Computational Problems
Stanford University CS254: Computational Complexity Handout 2 Luca Trevisan March 31, 2010 Last revised 4/29/2010 In this lecture we define NP, we state the P versus NP problem, we prove that its formulation
More informationDuality and Automata Theory
Duality and Automata Theory Mai Gehrke Université Paris VII and CNRS Joint work with Serge Grigorieff and Jean-Éric Pin Elements of automata theory A finite automaton a 1 2 b b a 3 a, b The states are
More informationCS 322 D: Formal languages and automata theory
CS 322 D: Formal languages and automata theory Tutorial NFA DFA Regular Expression T. Najla Arfawi 2 nd Term - 26 Finite Automata Finite Automata. Q - States 2. S - Alphabets 3. d - Transitions 4. q -
More informationKleene Algebras and Algebraic Path Problems
Kleene Algebras and Algebraic Path Problems Davis Foote May 8, 015 1 Regular Languages 1.1 Deterministic Finite Automata A deterministic finite automaton (DFA) is a model of computation that can simulate
More informationAlgebras and Bialgebras
Algebras and Bialgebras via categories with distinguished objects Vaughan Pratt Stanford University October 9, 2016 AMS Fall Western Sectional Meeting University of Denver, CO Vaughan Pratt (Stanford University)
More informationBringing class diagrams to life
Bringing class diagrams to life Luis S. Barbosa & Sun Meng DI-CCTC, Minho University, Braga & CWI, Amsterdam UML & FM Workshop 2009 Rio de Janeiro 8 December, 2009 Formal Methods proofs problems structures
More informationLogic: Propositional Logic (Part I)
Logic: Propositional Logic (Part I) Alessandro Artale Free University of Bozen-Bolzano Faculty of Computer Science http://www.inf.unibz.it/ artale Descrete Mathematics and Logic BSc course Thanks to Prof.
More informationPartial model checking via abstract interpretation
Partial model checking via abstract interpretation N. De Francesco, G. Lettieri, L. Martini, G. Vaglini Università di Pisa, Dipartimento di Ingegneria dell Informazione, sez. Informatica, Via Diotisalvi
More informationDuality in Logic. Duality in Logic. Lecture 2. Mai Gehrke. Université Paris 7 and CNRS. {ε} A ((ab) (ba) ) (ab) + (ba) +
Lecture 2 Mai Gehrke Université Paris 7 and CNRS A {ε} A ((ab) (ba) ) (ab) + (ba) + Further examples - revisited 1. Completeness of modal logic with respect to Kripke semantics was obtained via duality
More informationFoundations of Mathematics
Foundations of Mathematics Andrew Monnot 1 Construction of the Language Loop We must yield to a cyclic approach in the foundations of mathematics. In this respect we begin with some assumptions of language
More informationTheory of Computation
Theory of Computation (Feodor F. Dragan) Department of Computer Science Kent State University Spring, 2018 Theory of Computation, Feodor F. Dragan, Kent State University 1 Before we go into details, what
More informationFORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY
15-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY THURSDAY APRIL 3 REVIEW for Midterm TUESDAY April 8 Definition: A Turing Machine is a 7-tuple T = (Q, Σ, Γ, δ, q, q accept, q reject ), where: Q is a
More informationIntroduction. Foundations of Computing Science. Pallab Dasgupta Professor, Dept. of Computer Sc & Engg INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR
1 Introduction Foundations of Computing Science Pallab Dasgupta Professor, Dept. of Computer Sc & Engg 2 Comments on Alan Turing s Paper "On Computable Numbers, with an Application to the Entscheidungs
More informationPreliminaries. Chapter 3
Chapter 3 Preliminaries In the previous chapter, we studied coinduction for languages and deterministic automata. Deterministic automata are a special case of the theory of coalgebras, which encompasses
More informationCategorical logics for contravariant simulations, partial bisimulations, modal refinements and mixed transition systems
Categorical logics for contravariant simulations, partial bisimulations, modal refinements and mixed transition systems Ignacio Fábregas, Miguel Palomino, and David de Frutos-Escrig Departamento de Sistemas
More informationWhat are Iteration Theories?
What are Iteration Theories? Jiří Adámek and Stefan Milius Institute of Theoretical Computer Science Technical University of Braunschweig Germany adamek,milius @iti.cs.tu-bs.de Jiří Velebil Department
More informationOn a Monadic Encoding of Continuous Behaviour
On a Monadic Encoding of Continuous Behaviour Renato Neves joint work with: Luís Barbosa, Manuel Martins, Dirk Hofmann INESC TEC (HASLab) & Universidade do Minho October 1, 2015 1 / 27 The main goal A
More informationThe non-logical symbols determine a specific F OL language and consists of the following sets. Σ = {Σ n } n<ω
1 Preliminaries In this chapter we first give a summary of the basic notations, terminology and results which will be used in this thesis. The treatment here is reduced to a list of definitions. For the
More informationNOTES ON AUTOMATA. Date: April 29,
NOTES ON AUTOMATA 1. Monoids acting on sets We say that a monoid S with identity element ɛ acts on a set Q if q(st) = (qs)t and qɛ = q. As with groups, if we set s = t whenever qs = qt for all q Q, then
More informationFrom Monadic Second-Order Definable String Transformations to Transducers
From Monadic Second-Order Definable String Transformations to Transducers Rajeev Alur 1 Antoine Durand-Gasselin 2 Ashutosh Trivedi 3 1 University of Pennsylvania 2 LIAFA, Université Paris Diderot 3 Indian
More informationLecture 7. Logic. Section1: Statement Logic.
Ling 726: Mathematical Linguistics, Logic, Section : Statement Logic V. Borschev and B. Partee, October 5, 26 p. Lecture 7. Logic. Section: Statement Logic.. Statement Logic..... Goals..... Syntax of Statement
More informationA note on coinduction and weak bisimilarity for while programs
Centrum voor Wiskunde en Informatica A note on coinduction and weak bisimilarity for while programs J.J.M.M. Rutten Software Engineering (SEN) SEN-R9826 October 31, 1998 Report SEN-R9826 ISSN 1386-369X
More informationAbout the relationship between formal logic and complexity classes
About the relationship between formal logic and complexity classes Working paper Comments welcome; my email: armandobcm@yahoo.com Armando B. Matos October 20, 2013 1 Introduction We analyze a particular
More informationComputational Models - Lecture 1 1
Computational Models - Lecture 1 1 Handout Mode Ronitt Rubinfeld and Iftach Haitner. Tel Aviv University. February 29/ March 02, 2016 1 Based on frames by Benny Chor, Tel Aviv University, modifying frames
More informationHalting and Equivalence of Schemes over Recursive Theories
Halting and Equivalence of Schemes over Recursive Theories Dexter Kozen Computer Science Department, Cornell University, Ithaca, New York 14853-7501, USA Abstract Let Σ be a fixed first-order signature.
More informationSE 2FA3: Discrete Mathematics and Logic II. Teaching Assistants: Yasmine Sharoda,
SE 2FA3: Discrete Mathematics and Logic II Instructor: Dr. Ryszard Janicki, ITB 217, e-mail: janicki@mcmaster.ca, tel: 529-7070 ext: 23919, Teaching Assistants: Yasmine Sharoda, e-mail: sharodym@mcmaster.ca,
More informationWhat we have done so far
What we have done so far DFAs and regular languages NFAs and their equivalence to DFAs Regular expressions. Regular expressions capture exactly regular languages: Construct a NFA from a regular expression.
More informationRelational Interfaces and Refinement Calculus for Compositional System Reasoning
Relational Interfaces and Refinement Calculus for Compositional System Reasoning Viorel Preoteasa Joint work with Stavros Tripakis and Iulia Dragomir 1 Overview Motivation General refinement Relational
More informationOn regular languages over power sets
On regular languages over power sets Tim Fernando Trinity College Dublin, Ireland abstract The power set of a finite set is used as the alphabet of a string interpreting a sentence of Monadic Second-Order
More informationUnary Automatic Graphs: An Algorithmic Perspective 1
Unary Automatic Graphs: An Algorithmic Perspective 1 This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of
More informationPolynomial-time Computation via Local Inference Relations
Polynomial-time Computation via Local Inference Relations Robert Givan and David McAllester Robert Givan David McAllester Electrical & Computer Engineering P. O. Box 971 Purdue University AT&T Labs Research
More informationUsing topological systems to create a framework for institutions
Using topological systems to create a framework for institutions Sergejs Solovjovs Brno University of Technology 1/34 Using topological systems to create a framework for institutions Jeffrey T. Denniston
More informationApplications of Regular Algebra to Language Theory Problems. Roland Backhouse February 2001
1 Applications of Regular Algebra to Language Theory Problems Roland Backhouse February 2001 Introduction 2 Examples: Path-finding problems. Membership problem for context-free languages. Error repair.
More informationOverview. Systematicity, connectionism vs symbolic AI, and universal properties. What is systematicity? Are connectionist AI systems systematic?
Overview Systematicity, connectionism vs symbolic AI, and universal properties COMP9844-2013s2 Systematicity divides cognitive capacities (human or machine) into equivalence classes. Standard example:
More informationFUNCTORS AND ADJUNCTIONS. 1. Functors
FUNCTORS AND ADJUNCTIONS Abstract. Graphs, quivers, natural transformations, adjunctions, Galois connections, Galois theory. 1.1. Graph maps. 1. Functors 1.1.1. Quivers. Quivers generalize directed graphs,
More informationA categorical view of computational effects
Emily Riehl Johns Hopkins University A categorical view of computational effects C mp se::conference 1. Functions, composition, and categories 2. Categories for computational effects (monads) 3. Categories
More informationThe Pumping Lemma. for all n 0, u 1 v n u 2 L (i.e. u 1 u 2 L, u 1 vu 2 L [but we knew that anyway], u 1 vvu 2 L, u 1 vvvu 2 L, etc.
The Pumping Lemma For every regular language L, there is a number l 1 satisfying the pumping lemma property: All w L with w l can be expressed as a concatenation of three strings, w = u 1 vu 2, where u
More informationFinite Automata - Deterministic Finite Automata. Deterministic Finite Automaton (DFA) (or Finite State Machine)
Finite Automata - Deterministic Finite Automata Deterministic Finite Automaton (DFA) (or Finite State Machine) M = (K, Σ, δ, s, A), where K is a finite set of states Σ is an input alphabet s K is a distinguished
More informationPolynomial-time Computation via Local Inference Relations
Polynomial-time Computation via Local Inference Relations ROBERT GIVAN Purdue University and DAVID MCALLESTER AT&T Labs Research We consider the concept of a local set of inference rules. A local rule
More informationA few bridges between operational and denotational semantics of programming languages
A few bridges between operational and denotational semantics of programming languages Soutenance d habilitation à diriger les recherches Tom Hirschowitz November 17, 2017 Hirschowitz Bridges between operational
More informationA Graph Rewriting Semantics for the Polyadic π-calculus
A Graph Rewriting Semantics for the Polyadic π-calculus BARBARA KÖNIG Fakultät für Informatik, Technische Universität München Abstract We give a hypergraph rewriting semantics for the polyadic π-calculus,
More informationDecidability: Church-Turing Thesis
Decidability: Church-Turing Thesis While there are a countably infinite number of languages that are described by TMs over some alphabet Σ, there are an uncountably infinite number that are not Are there
More informationOutline. Complexity Theory. Example. Sketch of a log-space TM for palindromes. Log-space computations. Example VU , SS 2018
Complexity Theory Complexity Theory Outline Complexity Theory VU 181.142, SS 2018 3. Logarithmic Space Reinhard Pichler Institute of Logic and Computation DBAI Group TU Wien 3. Logarithmic Space 3.1 Computational
More informationHKN CS/ECE 374 Midterm 1 Review. Nathan Bleier and Mahir Morshed
HKN CS/ECE 374 Midterm 1 Review Nathan Bleier and Mahir Morshed For the most part, all about strings! String induction (to some extent) Regular languages Regular expressions (regexps) Deterministic finite
More informationProof systems for Moss coalgebraic logic
Proof systems for Moss coalgebraic logic Marta Bílková, Alessandra Palmigiano, Yde Venema March 30, 2014 Abstract We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced
More informationA proof theoretical account of polarity items and monotonic inference.
A proof theoretical account of polarity items and monotonic inference. Raffaella Bernardi UiL OTS, University of Utrecht e-mail: Raffaella.Bernardi@let.uu.nl Url: http://www.let.uu.nl/ Raffaella.Bernardi/personal
More information(Co-)algebraic Automata Theory
(Co-)algebraic Automata Theory Sergey Goncharov, Stefan Milius, Alexandra Silva Erlangen, 5.11.2013 Chair 8 (Theoretical Computer Science) Short Histrory of Coalgebraic Invasion to Automata Theory Deterministic
More informationarxiv: v1 [cs.ds] 9 Apr 2018
From Regular Expression Matching to Parsing Philip Bille Technical University of Denmark phbi@dtu.dk Inge Li Gørtz Technical University of Denmark inge@dtu.dk arxiv:1804.02906v1 [cs.ds] 9 Apr 2018 Abstract
More informationMonoidal Categories, Bialgebras, and Automata
Monoidal Categories, Bialgebras, and Automata James Worthington Mathematics Department Cornell University Binghamton University Geometry/Topology Seminar October 29, 2009 Background: Automata Finite automata
More informationEECS 144/244: Fundamental Algorithms for System Modeling, Analysis, and Optimization
EECS 144/244: Fundamental Algorithms for System Modeling, Analysis, and Optimization Discrete Systems Lecture: Automata, State machines, Circuits Stavros Tripakis University of California, Berkeley Stavros
More informationUniversität Augsburg
Universität Augsburg Properties of Overwriting for Updates in Typed Kleene Algebras Thorsten Ehm Report 2000-7 Dezember 2000 Institut für Informatik D-86135 Augsburg Copyright c Thorsten Ehm Institut für
More informationTree Automata and Rewriting
and Rewriting Ralf Treinen Université Paris Diderot UFR Informatique Laboratoire Preuves, Programmes et Systèmes treinen@pps.jussieu.fr July 23, 2010 What are? Definition Tree Automaton A tree automaton
More informationContext Free Grammars
Automata and Formal Languages Context Free Grammars Sipser pages 101-111 Lecture 11 Tim Sheard 1 Formal Languages 1. Context free languages provide a convenient notation for recursive description of languages.
More informationQuasi-Boolean Encodings and Conditionals in Algebraic Specification
Quasi-Boolean Encodings and Conditionals in Algebraic Specification Răzvan Diaconescu Institute of Mathematics Simion Stoilow of the Romanian Academy Abstract We develop a general study of the algebraic
More informationPOL502: Foundations. Kosuke Imai Department of Politics, Princeton University. October 10, 2005
POL502: Foundations Kosuke Imai Department of Politics, Princeton University October 10, 2005 Our first task is to develop the foundations that are necessary for the materials covered in this course. 1
More informationPartially ordered monads and powerset Kleene algebras
Partially ordered monads and powerset Kleene algebras Patrik Eklund 1 and Werner Gähler 2 1 Umeå University, Department of Computing Science, SE-90187 Umeå, Sweden peklund@cs.umu.se 2 Scheibenbergstr.
More informationExtensions to the Logic of All x are y: Verbs, Relative Clauses, and Only
1/53 Extensions to the Logic of All x are y: Verbs, Relative Clauses, and Only Larry Moss Indiana University Nordic Logic School August 7-11, 2017 2/53 An example that we ll see a few times Consider the
More informationComputational Models #1
Computational Models #1 Handout Mode Nachum Dershowitz & Yishay Mansour March 13-15, 2017 Nachum Dershowitz & Yishay Mansour Computational Models #1 March 13-15, 2017 1 / 41 Lecture Outline I Motivation
More informationAn introduction to Yoneda structures
An introduction to Yoneda structures Paul-André Melliès CNRS, Université Paris Denis Diderot Groupe de travail Catégories supérieures, polygraphes et homotopie Paris 21 May 2010 1 Bibliography Ross Street
More informationEquational Theory of Kleene Algebra
Introduction to Kleene Algebra Lecture 7 CS786 Spring 2004 February 16, 2004 Equational Theory of Kleene Algebra We now turn to the equational theory of Kleene algebra. This and the next lecture will be
More informationNotes for Lecture Notes 2
Stanford University CS254: Computational Complexity Notes 2 Luca Trevisan January 11, 2012 Notes for Lecture Notes 2 In this lecture we define NP, we state the P versus NP problem, we prove that its formulation
More informationNotes on Monoids and Automata
Notes on Monoids and Automata Uday S. Reddy November 9, 1994 In this article, I define a semantics for Algol programs with Reynolds s syntactic control of interference?;? in terms of comonoids in coherent
More informationAutomata Theory and Formal Grammars: Lecture 1
Automata Theory and Formal Grammars: Lecture 1 Sets, Languages, Logic Automata Theory and Formal Grammars: Lecture 1 p.1/72 Sets, Languages, Logic Today Course Overview Administrivia Sets Theory (Review?)
More information