summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/principia/principia.sty
blob: 14a99d9fa3b394a8645d3f5a4b0b68df2251bd1e (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
%Package Identification
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{principia}[2020/10/25 principia package version 1.1] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
%Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24
%Version 1.1 (updates): fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
%Licensed under LaTeX Project Public License 1.3c. 
%Copyright Landon D. C. Elkind, 2020.  (https://landondcelkind.com/contact/).

%Principia package requirements
\RequirePackage{amssymb} %This loads the relation domain and converse domain limitation symbols.
\RequirePackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc.
\RequirePackage{graphicx} %This loads commands that flip iota for definite descriptions, Lambda for the universal class, and so on. The (superseded) graphics package should also work here, but is not recommended.
\RequirePackage{marvosym} %This loads the male and female symbol.
\RequirePackage{pifont} %This loads the symbols such as the eight-pointed asterisk.

%Meta-logical symbols
\newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions.
\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.
\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof.
\newcommand{\pmhp}{\text{Hp}} %This typesets Hp (short for antecedent), which occurs at the beginning of a proof.
\newcommand{\pmprop}{\text{Prop}} %This occurs at the end of a proof.
\newcommand{\pmithm}{\pmimp\;\pmthm} %This occurs when a meta-theoretic implication is asserted.
\newcommand{\pmbr}[1]{\bigg \lbrack \normalsize #1 \bigg \rbrack} %These are larger brackets for substitution.
\newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}  \bigg \rbrack} %This is the substitution command.
\newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}  \bigg \rbrack} %This is the substitution command.
\newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}  \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}  \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}  \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}  \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command.
\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command.
\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command.
\newcommand{\pmsUbbbb}[8]{\small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.
\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command.
\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command.
\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command.
\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.
\newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign.
\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number.
\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number.
\newcommand{\pmiddf}{\mathbin{=}}
\newcommand{\pmdf}{\quad \text{Df}}
\newcommand{\pmpp}{\quad \text{Pp}}

%Square dots for scope, defined for up to six dots
\newcommand{\pmdot}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}}
\newcommand{\pmdott}{\mathrel{\overset{\pmdot}{\pmdot}}}
\newcommand{\pmdottt}{\pmdott\hspace{.1em}\pmdot}
\newcommand{\pmdotttt}{\pmdott\hspace{.1em}\pmdott}
\newcommand{\pmdottttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdot}
\newcommand{\pmdotttttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdott}

%Logical connectives
\newcommand{\pmnot}{\mathord{\ooalign{$\boldsymbol{\sim}\mkern.5mu$\hidewidth\cr$\boldsymbol{\sim}$\cr\hidewidth$\mkern.5mu\boldsymbol{\sim}$}}}
\newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}}
\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}}
\newcommand{\pmor}{\mathbin{\ooalign{$\boldsymbol{\vee}\mkern.5mu$\hidewidth\cr$\boldsymbol{\vee}$\cr\hidewidth$\mkern.5mu\boldsymbol{\vee}$}}}
\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}}
\newcommand{\pmall}[1]{(#1)}
\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)}
\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}}
\newcommand{\pmandd}{\overset{\pmand}{\pmand}}
\newcommand{\pmanddd}{\pmandd\hspace{.1em}\pmand}
\newcommand{\pmandddd}{\pmandd\hspace{.1em}\pmandd}
\newcommand{\pmanddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmand}
\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd}

%Additional defined logic signs
\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}
\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable
\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables
\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables
\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions
\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable
\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables
\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables
\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.01
\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions
\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01
\newcommand{\pmDsc}{\pmiota} %*14.01
\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02

%Class signs
\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}
\newcommand{\pmcnull}{\Lambda}
\newcommand{\pmcls}[2]{\pmhat{#1}(#2)}
\newcommand{\pmCls}{\text{Cls}}
\newcommand{\pmClsn}[1]{\text{Cls}^{#1}}
\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}}
\newcommand{\pmccmp}[1]{\boldsymbol{-}#1}
\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2}
\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}}
\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}}
\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}}
\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}}

%Relation signs
\newcommand{\pmruni}{\dot{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}}
\newcommand{\pmrnull}{\dot{\Lambda}}
\newcommand{\pmdscf}[2]{#1\textbf{`}#2}
\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2}
\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2}
\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2}
\newcommand{\pmdscfR}[1]{#1_{\pmcin}}
\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}}
\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1}
\newcommand{\pmDm}{\text{D}}
\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1}
\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}}
\newcommand{\pmcmp}[1]{C\textbf{`}#1}
\newcommand{\pmCmp}{C}
\newcommand{\pmfld}[1]{F\textbf{`}#1}
\newcommand{\pmFld}{F}
\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3}
\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5}
\newcommand{\pmrelep}[3]{#1\{#2\}#3}
\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccmp}$}#1}
\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccmp}$}}#2}
\newcommand{\pmrexists}{\dot{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}}
\newcommand{\pmcrel}[1]{\breve{#1}}
\newcommand{\pmCnv}{\text{Cnv}}
\newcommand{\pmcnv}[1]{\breve{#1}}
\newcommand{\pmcnvr}[1]{\text{Cnv}\textbf{`}#1}
\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\cdot\hidewidth$\cr$\mathbf{\pmccup}$}}}
\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccap}$}}}
\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\cdot\hidewidth$\cr$\mathbf{\pmcinc}$}}}
\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2}
\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}}
\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2}
\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}}
\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1}
\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1}
\newcommand{\pmSg}{\text{sg}}
\newcommand{\pmGs}{\text{gs}}
\newcommand{\pmRprd}{\mathop{|}}
\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}}
\newcommand{\pmrprdn}[2]{#1^{#2}}
\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2}
\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2}
\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3}
\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2}
\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2}
\newcommand{\pmop}{\mathop{\text{\Female}}}
\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2}

%Products and sums of classes of classes or relations
\newcommand{\pmccsum}[1]{p\textbf{`}#1}
\newcommand{\pmccprd}[1]{s\textbf{`}#1}
\newcommand{\pmcrsum}[1]{\dot{p}\textbf{`}#1}
\newcommand{\pmcrprd}[1]{\dot{s}\textbf{`}#1}
\newcommand{\pmRprdd}{\mathop{||}}
\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}}

%Identity and Diversity
\newcommand{\pmrid}{I}
\newcommand{\pmrdiv}{J}
\newcommand{\pmcunit}[1]{\iota\textbf{`}#1}
\newcommand{\pmcUnit}{\iota}
\newcommand{\pmcunits}[1]{\breve{\iota}\textbf{`}#1}

%Cardinal numbers
\newcommand{\pmcn}[1]{#1}

%Ordinal numbers
\newcommand{\pmrn}[1]{#1_r}
\newcommand{\pmdn}[1]{\dot{#1}}
\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2}

%Subclasses and subrelations
\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1}
\newcommand{\pmsCl}{\text{Cl}}
\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1}
\newcommand{\pmsCle}{\text{Cl ex}}
\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1}
\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1}
\newcommand{\pmsRl}{\text{Rl}}
\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1}
\newcommand{\pmsRle}{\text{Rl ex}}
\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1}
\newcommand{\pmRel}{\text{Rel}}
\newcommand{\pmReln}[1]{\text{Rel}^{#1}}
\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}}

%Relative type symbols
\newcommand{\pmrt}[1]{t\textbf{`}#1}
\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2}
\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2}
\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2}
\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2}
\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3}
\newcommand{\pmrtric}[3]{^{#1}t_{#2}\textbf{`}#3}
\newcommand{\pmrtdi}[2]{#1_{#2}}
\newcommand{\pmrtdc}[2]{#1(#2)}
\newcommand{\pmrtdri}[2]{#1_{#2}}
\newcommand{\pmrtdrc}[2]{#1(#2)}

%Similarity relation signs
\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2}
\newcommand{\pmsm}{\mathrel{\text{sm}}}
\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}}
\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}}
\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls}
\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1}
\newcommand{\pmoneone}{1\boldsymbol{\to}1}

%Selections
\newcommand{\pmselp}[1]{P_{\small\Delta}\mathbf{`}#1}
\newcommand{\pmSelp}{P_{\Delta}}
\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\mathbf{`}#1}
\newcommand{\pmSele}{\pmcin_{\Delta}}
\newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1}
\newcommand{\pmSelf}{F_{\Delta}}
\newcommand{\pmex}[1]{\text{Cls} \mathop{\text{excl}}\mathbf{`}#1}
\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}}
\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1}
\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}}
\newcommand{\pmselc}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}} #2}
\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}}
\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}}
\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}}

%Inductive relations
\newcommand{\pmanc}[1]{#1_\pmast}
\newcommand{\pmancc}[1]{\pmcnv{#1}_\pmast}
\newcommand{\pmrst}[1]{#1_\text{st}}
\newcommand{\pmrts}[1]{#1_\text{ts}}
\newcommand{\pmpot}[1]{\text{Pot}\mathbf{`}#1}
\newcommand{\pmpotid}[1]{\text{Potid}\mathbf{`}#1}
\newcommand{\pmpo}[1]{#1_\text{po}}
\newcommand{\pmB}{B}
\newcommand{\pmmin}[1]{\text{min}_{#1}}
\newcommand{\pmmax}[1]{\text{max}_{#1}}
\newcommand{\pmMin}{\text{min}}
\newcommand{\pmMax}{\text{max}}
\newcommand{\pmgen}[1]{\text{gen}\mathbf{`}#1}
\newcommand{\pmGen}{\text{gen}}
\newcommand{\pmefr}[2]{#1\pmast#2}
\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2}
\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2}
\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2}

%Cardinality 
\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1}
\newcommand{\pmNc}{\text{Nc}}
\newcommand{\pmNC}{\text{NC}}
\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1}
\newcommand{\pmNoc}{\text{N}_0\text{c}}
\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1}
\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}}

\newcommand{\pmclsrefl}{\text{Cls} \mathop{\text{refl}}} 
\newcommand{\pmncrefl}{\text{NC} \mathop{\text{refl}}}