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Capitolul 6, Pagina 203, Exercitiul 10

the mad hatter — Wed, 21 Dec 2011 01:09:31 +0000

1(1) (Ex)(Fx <-> Gx) Pr.
2(2) (Ax)(Gx -> (Hx -> Jx)) Pr.
3(3) Fa <-> Ga As.
3(4) (Fa -> Ga) & (Ga -> Fa) 3Df
3(5) Fa -> Ga 4E&
3(6) Ga -> Fa 4E& (inutila)
2(7) Ga -> (Ha -> Ja) 2EA
3(8) ~Fa v Ga 5IS(IMP)
3(9) ~Ga v Fa 6IS(IMP) (inutila)
10(10) ~Fa As.
10(11) (Ex)~Fx 10IE
10(12) ~(Ax)Fx 11IS(QS)
10(13) (Ax)Fx -> (Ex)(Gx & ~Hx) 12IS(PIM)
10(14) (Ex)Jx v [(Ax)Fx -> (Ex)(Gx & ~Hx)] 13IV
15(15) Ga As.
2,15(16) Ha -> Ja 8,15E->
2,15(17) ~Ha v Ja 16IS(IMP)
18(18) ~Ha As.
15,18(19) Ga & ~Ha 15,18I&
15,18(20) (Ex)(Gx & ~Hx) 19IE
15,18(21) (Ax)Fx -> (Ex)(Gx & ~Hx) 20IS(PIM)
15,18(22) (Ex)Jx v [(Ax)Fx -> (Ex)(Gx & ~Hx)] 21IV
23(23) Ja As.
23(24) (Ex)Jx 23IE
23(25) (Ex)Jx v [(Ax)Fx -> (Ex)(Gx & ~Hx)] 24 IV
2,15(26) (Ex)Jx v [(Ax)Fx -> (Ex)(Gx & ~Hx)] 17,18,22,23,23EV
2,3(27) (Ex)Jx v [(Ax)Fx -> (Ex)(Gx & ~Hx)] 8,10,14,15,26 EV
1,2(28) (Ex)Jx v [(Ax)Fx -> (Ex)(Gx & ~Hx)] 1,3,27 EE

Capitolul 6, Pagina 203, Exercitiul 21

the mad hatter — Tue, 20 Dec 2011 23:53:39 +0000

1(1) (Ex)(Ay)(Fy -> Gx) Pr.
2(2) (Ay)(Fy -> Ga) As.
2(3) Fb -> Ga 2EA
2(4) (Ey)(Fb -> Gy) 3IE
2(5) (Ax)(Ey)(Fx -> Gy) 4IA
1(6) (Ax)(Ey)(Fx -> Gy) 1,2,5EE

Capitolul 6, Pagina 203, Exercitiul 18

the mad hatter — Tue, 20 Dec 2011 23:44:03 +0000

1(1) (Ax)(Ey)(Fx -> Gy) Pr.
2(2) (Ax)(Ey)(~Fx -> Gy) Pr.
1(3) (Ey)(Fa -> Gy) 1EA
2(4) (Ey)(~Fa -> Gy) 2EA
5(5) Fa -> Ga As.
6(6) ~Fa -> Ga As.
7(7) ~Ga As.
5,7(8) ~Fa 5,7IS(MT)
6,7(9) ~~Fa 6,7IS(MT)
6,7(10) Fa 9DN
5,6,7(11) ^ 8,10E~
2,5,7(12) ^ 4,6,11EE
1,2,7(13) ^ 3,5,12EE
1,2(14) ~~Ga 7,13I~
1,2(15) Ga 14DN
1,2(16) (Ez)Gz 1515IE

Capitolul 6, Pagina 203, Exercitiul 14

the mad hatter — Tue, 20 Dec 2011 23:30:16 +0000

1(1) (Ax)(Fx -> (Ey)Gy) Pr.
2(2) (Ax)(~Fx -> (Ey)Gy) Pr.
1(3) Fa -> (Ey)Gy 1EA
2(4) ~Fa -> (Ey)Gy 2EA
5(5) ~(Ey)Gy As.
1,5(6) ~Fa 3,5IS(MT)
2,5(7) ~~Fa 4,5IS(MT)
2,5(8) Fa 7DN
1,2,5(9) ^ 6,8E~
1,2(10) ~~(Ey)Gy 5,9I~
1,2(11) (Ey)Gy 10DN
12(12) Ga As.
12(13) (Ez)Gz 12IE
1,2(14) (Ez)Gz 11,12,13EE

Capitolul 6, Pagina 203, Exercitiul 11

the mad hatter — Tue, 20 Dec 2011 23:05:41 +0000

1(1) (Ax)(Fx & (Ey)Gy) Pr.
1(2) Fa & (Ey)Gy 1EA
1(3) Fa 2EA
1(4) (Ey)Gy 2EA
5(5) Ga 3,5I&
1,5(6) Fa & Ga 3,5I&
1,5(7) (Ex)(Fx & Gx) 6IE
1(8) (Ex)(Fx & Gx) 4,5,7EE

Capitolul 4, Pagina 119, Exercitiul 11

the mad hatter — Wed, 23 Nov 2011 13:26:14 +0000

1(1) A -> B Pr.
2(2) B -> C Pr.
3(3) C -> A Pr.
4(4) B As.
2,4(5) C 2,4E->
2,3,4(6) A 3,5E->
2,3(7) B -> A 4,6I->
1,2,3(8) (A -> B) & (B -> A) 1,7I&
1,2,3(9) A <-> B 8Df.
10(10) C As.
3,10(11) A 3,10E->
1,3,10(12) B 1,11E->
1,3(13) C -> B 10,12I->
1,2,3(14) (B -> C) & (C -> B) 2,13I&
1,2,3(15) B <-> C 14Df.
16(16) A As.
1,16(17) B 1,16E->
1,2,16(18) C 2,17E->
1,2(19) A -> C 16,18I->
1,2,3(20) (C -> A) & (A -> C) 3,19I&
1,2,3(21) C <-> A 20Df.
1,2,3(22) (B <-> C) & (C <-> A) 15,21I&
1,2,3(23) A <-> B & ((B <-> C) & (C <-> A)) 9,22I&

Capitolul 4, Pagina 116, Exercitiul 22

the mad hatter — Wed, 23 Nov 2011 12:47:59 +0000

1(1) A -> (~B v ~C) Pr.
2(2) ~C -> ~D Pr.
3(3) B Pr.
4(4) ~(~A v ~D) As.
5(5) A As.
1,5(6) ~B v ~C 1,5E->
7(7) ~B As.
3,7(8) ^ 3,7E~
3,7(9) ~A 3,8I~
3,7(10) ~A v ~D 3Iv
3,4,7(11) ^ 4,10E~
12(12) ~C As.
2,12(13) ~D 2,12E->
2,12(14) ~A v ~D 13Iv
2,4,12(15) ^ 4,14E~
1,2,3,4,5(16) ^ 6,7,11,12,15EV
1,2,3,4(17) ~A 5,16I~
1,2,3,4(18) ~A v ~D 17Iv
1,2,3,4(19) ^ 5,18E~
1,2,3(20) ~~(~A v ~D) 4,19I~
1,2,3(21) ~A v ~D 20DN

Dynamic Epistemic Logic Links

the mad hatter — Sat, 23 Jul 2011 17:23:01 +0000

Agotnes, Wooldridge, van der Hoek, Quantifying Over Coalitions in Epistemic Logic

Thomas Agotnes, Hans van Ditmarsch, What Will They Say ?– Public Announcement Games

Patrick Allo, A Modal Perspective on Proof Dynamics

Guillaume Aucher, Consistency preservation and crazy formulas in BMS ?

Baltag, A Logic of Epistemic Actions

Baltag, Coecke, Sadrzadeh, Reasoning about Dynamic Epistemic Logic

Baltag, Smets, Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision

Baltag, Sadrzadeh, , The Algebra of Multi-Agent Dynamic Belief Revision

Balbiani, Baltag, Ditmarsch, ‘Knowable’ as ‘known after an announcement

Balbiani, Baltag, Ditmarsch, Herzig, Hoshi, de Lima, What can we achieve by arbitrary announcements?

Philippe Balbiani, Hans van Ditmarsch, Andreas Herzig and Tiago de Lima, A tableau method for public announcement logics

Johan van Benthem, OPEN PROBLEMS IN LOGICAL DYNAMICS

Samuel Bucheli, Roman Kuznets, Bryan Renne, Joshua Sack, Thomas Studer,Justied Belief Change

Bucheli, Kuznets, Studer, Partial Realization in Dynamic Justification Logic

Hans van Ditmarsch, Dynamic Epistemic Logic, Protocols, and Security

Ditmarsch, van der Hoek, Kooi, Playing cards with Hintikka. An introduction to dynamic epistemic logic

Hans van Ditmarsch, Dynamic Epistemic Logic, Protocols, and Security

Hans van Ditmarsch, [slides] Dynamic epistemic logic, the Moore-sentence, the Fitch paradox, and a logic puzzle

Hans van Ditmarsch, Barteld Kooi, Wiebe van der Hoek, Dynamic Epistemic Logic , Link2

Hans van Ditmarsch, Wiebe van der Hoek, Petar Iliev,Everything is Knowable — how to get to know whether a proposition is true

Hans van Ditmarsch, Ruan, Verbrugge, Sum and Product in Dynamic Epistemic Logic

Hans van Ditmarsch, Belief Change and Dynamic Logic

Jan van Eijck, Yet More Modal Logics of Preference Change and Belief Revision

Jan van Eijck, Floor Sietsma, Message Passing in a Dynamic Epistemic Logic Setting

Jan van Eijck, Simona Orzan, Modelling the Epistemics of Communication with Functional Programming

Jelle Gerbrandy, Dynamic Epistemic Logic

Jelle Gerbrandy, Willem Groeneveld, Reasoning about Information Change

Brian Hill, Dynamic Awareness

Wes Holliday and Thomas Icard [slides], Moorean Phenomena in Epistemic Logic

Wesley H. Holliday and Thomas F. Icard, III, Moorean Phenomena in Epistemic Logic ?

Holliday, Hoshi, Icard, Schematic Validity in Dynamic Epistemic Logic : Decidability

Hoshi, Yap, ETL, DEL, and Past Operators

Barteld Kooi, Expressivity and completeness for public update logics via reduction axioms

Tiago De Lima, Epistemic Actions and Ontic Actions: a Uniﬁed Logical Framework (extended version)

Khaled Mellouli (Ed.) Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Ben Rodenhauser, Intentions in Interaction

Bryan Renne, Dynamic Epistemic Logic with Justification

Bryan Renne, A Survey of Dynamic Epistemic Logic

Bryan Renne, Public Communication in Justiﬁcation Logic

Bryan Renne, The Relative Expressivity of Public and Private Communication in BMS Logic

?, Interactive Models of Closure and Introspection

A dynamic take on Fitch’s knowability

David Steiner, Thomas Studer, Total Public Announcements;

Yanjing Wang, Epistemic Modelling and Protocol Dynamics;

Yanjing Wang, Floor Sietsma, Jan van Eijck, Logic of Information Flow on Communication Channels

LaTeX tikz Graphic for Muddy Children Puzzle

the mad hatter — Thu, 21 Apr 2011 22:57:14 +0000

LaTeX graphic using tikz for a public announcement logic solution to the Muddy Children Puzzle (van Ditmarsch & B. Kooi - Dynamic Epistemic Logic, Springer, 2007, page 94). Use the code below and you’ll obtain something like this:

\documentclass[11pt]{article}

\parindent=.25in

\parskip=2ex

\usepackage{amsthm}

\usepackage{amsbsy}

\usepackage{amssymb}

\usepackage{amsfonts}

\usepackage{amsmath}

\usepackage{setspace} %pt spatiere

\usepackage{graphicx}

\usepackage{pgf}

\usepackage{tikz}

\usetikzlibrary{arrows,automata,positioning}

\usetikzlibrary{matrix,arrows}

\usepackage{verbatim}

\begin{document}

%\pagestyle{empty}

%created by alexandru dragomir, feel free to use it

\pagenumbering{arabic}

\pagestyle{plain}

%\maketitle

\newpage

\begin{tikzpicture}[scale=.5, transform shape]

%\tikzstyle{every node} = [circle, fill=gray!30]

\tikzstyle{every node} = [circle, fill=white]

\node (a) at (0, 0) {000};

\node (b) at (5,0) {100};

\node (c) at (2,2) {001};

\node (d) at (7,2) {101};

\node (e) at (0,4.5) {010};

\node (f) at (5,4.5) {\underline{110}};

\node (g) at (2,6.5) {011};

\node (h) at (7,6.5) {111};

\path (a) edge node {$a$} (b);

\path (a) edge node {$b$} (e);

\path (a) edge node {$c$} (c);

\path (e) edge node {$a$} (f);

\path (e) edge node {$c$} (g);

\path (c) edge node {$b$} (g);

\path (c) edge node {$a$} (d);

\path (b) edge node {$c$} (d);

\path (g) edge node {$a$} (h);

\path (h) edge node {$b$} (d);

\path (h) edge node {$c$} (f);

\path (f) edge node {$b$} (b);

\node (p11) at (8,3){};

\node (p12) at (14,3){};

\path[dotted, ->] (p11) edge node{} (p12);

\node (b2) at (20,0) {100};

\node (c2) at (17,2) {001};

\node (d2) at (22,2) {101};

\node (e2) at (15,4.5) {010};

\node (f2) at (20,4.5) {\underline{110}};

\node (g2) at (17,6.5) {011};

\node (h2) at (22,6.5) {111};

\path (e2) edge node {$a$} (f2);

\path (e2) edge node {$c$} (g2);

\path (c2) edge node {$b$} (g2);

\path (c2) edge node {$a$} (d2);

\path (b2) edge node {$c$} (d2);

\path (g2) edge node {$a$} (h2);

\path (h2) edge node {$b$} (d2);

\path (h2) edge node {$c$} (f2);

\path (f2) edge node {$b$} (b2);

\node (p21) at (18,-1){};

\node (p22) at (18,-7){};

\path[dotted, ->](p21) edge node{} (p22);

\node (d3) at (22,-12.5) {101};

\node (f3) at (20,-10.5) {\underline{110}};

\node (g3) at (17,-8) {011};

\node (h3) at (22,-8) {111};

\path (g3) edge node {$a$} (h3);

\path (h3) edge node {$b$} (d3);

\path (h3) edge node {$c$} (f3);

\node (p31) at (8,-9){};

\node (p32) at (14,-9){};

\path[dotted, ->] (p32) edge node{} (p31);

\node (f4) at (5,-10.5) {\underline{110}};

\end{tikzpicture}

\end{document}

Revista: Logic and Logical Philosophy

the mad hatter — Sun, 28 Nov 2010 23:18:11 +0000

Foarte multe articole interesante, aici: http://www.logika.umk.pl/llp/pi.html