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"data": "::::header\n:::hgroup\n::p[Logika pre informatikov]{.h2.text-muted}\n# 1. teoretické cvičenie\n:::\n\n:::div{.dl-indented}\n:icon[diagram-2-fill]{.text-primary} Vetva repozitára\n: tc01\n: :strong[:icon[arrow-clockwise] Otvoriť toto cvičenie v správnej vetve]\n\n:icon[save-fill]{.text-success} Uloženie riešenia do vetvy\n: Stlačte :span[Merge changes]{.border.border-success.text-success.p-1.rounded} na hornej lište.\n: Uložte svoje riešenie pred zavretím karty prehliadača alebo odchodom na inú stránku!\n\n:icon[help] Návod\n: Krátky návod na použitie aplikácie Logic Workbook nájdete na konci tohto hárku.\n\n:icon[envelope-at-fill]{.text-primary} Kontakt na vyučujúcich\n: lpi-team :icon[at] lists.dai.fmph.uniba.sk.\n\n:icon[person-raised-hand]{.text-primary} Konzultačné hodiny\n: Streda o 12:20–13:10 v I-9\n:::\n::::",
"comments": []
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{
"id": 48,
"type": "text",
"data": "## :icon[bonus] Domáca úloha\n\nĎalšie skúsenosti a spätnú väzbu môžete získať vyriešením domácej úlohy.\n\n::::div{.dl-indented}\n1. domáca úloha\n: :::div{.dl-indented}\n :icon[file-earmark-ruled-fill]{.text-primary} Pracovný hárok\n : du01 :small[(odkaz otvorí hárok v správnej vetve)]\n\n :icon[deadline] Termín odovzdania\n : nedeľa 1. 3. 2026 o 23:59:59\n :::\n::::",
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{
"id": 54,
"type": "context",
"data": [
{
"id": 56,
"type": "text",
"data": "## Cvičenie 1.:cnt[a]\n\n:small[:icon[source]\nZbierka:\n:xref[1.1.1]{.exbook label="príklad"},\n:xref[1.1.5]{.exbook label="úloha"}.]\n\nUvažujme jazyk $\Lang$ logiky prvého rádu s množinami symbolov:",
"comments": []
},
{
"id": 55,
"type": "context/language",
"data": {
"constants": "Alex, Betty, Charles, Dana, Ed, Gina, dad",
"predicates": "woman/1, parent/2, child/3, older/2",
"functions": ""
},
"contextExtension": {
"constants": [
"Alex",
"Betty",
"Charles",
"Dana",
"Ed",
"Gina",
"dad"
],
"predicates": [
{
"name": "woman",
"arity": 1
},
{
"name": "parent",
"arity": 2
},
{
"name": "child",
"arity": 3
},
{
"name": "older",
"arity": 2
}
],
"functions": []
},
"comments": []
},
{
"id": 57,
"type": "text",
"data": "Zamýšľanou doménou tohto jazyka sú ľudia\na zamýšľaný význam predikátových symbolov je nasledovný:\n\n:::div{.table.table-intended-meaning}\n| Predikát | Význam |\n|----------|--------|\n| & (ampersand).\n:::",
"comments": []
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{
"id": 40,
"type": "formalizationChecker",
"data": {
"exercise": {
"exercise_id": 29,
"title": "2024 – Cvičenie 1.4",
"description": "Sformalizujte nasledujúce výroky ako atomické formuly vo vyššie opísanom jazyku logiky prvého rádu. Ak je na vyjadrenie výroku potrebných viacero atomických formúl, spojte ich znakom &. ",
"constants": "A, excellent, E, sufficient, Eugen, Lucia, Math, Peter, PhysEd",
"predicates": "got_grade/4, likes/2, man/1, compulsory/1, course/1, older/2, student/1, teaches/2, elective/1, woman/1",
"functions": "",
"constraints": "",
"propositions": [
{
"proposition_id": 1197,
"proposition": "1. Peter je muž.",
"solution": ""
},
{
"proposition_id": 1198,
"proposition": "2. Peter je študent.",
"solution": null
},
{
"proposition_id": 1199,
"proposition": "3. Lucia je žena a študentka.",
"solution": null
},
{
"proposition_id": 1200,
"proposition": "4. Lucia je staršia ako Peter.",
"solution": null
},
{
"proposition_id": 1201,
"proposition": "5. Matematiku učí Eugen.",
"solution": null
},
{
"proposition_id": 1202,
"proposition": "6. Peter a Lucia sú od neho mladší.",
"solution": null
},
{
"proposition_id": 1203,
"proposition": "7. Peter dostal z Matematiky od Eugena známku E.",
"solution": null
},
{
"proposition_id": 1204,
"proposition": "8. Lucia má rada Petra.",
"solution": null
},
{
"proposition_id": 1205,
"proposition": "9. Aj keď má (ona) z Matematiky od Eugena známku výborný.",
"solution": null
},
{
"proposition_id": 1206,
"proposition": "10. Známka výborný je len iný názov pre A-čko, a podobne dostatočný značí to isté ako E-čko.",
"solution": null
},
{
"proposition_id": 1207,
"proposition": "11. Eugen sa má rád.",
"solution": null
},
{
"proposition_id": 1208,
"proposition": "12. Matematika je povinný predmet.",
"solution": null
},
{
"proposition_id": 1209,
"proposition": "13. Všetci vyššie menovaní študenti majú radi Telocvik.",
"solution": null
},
{
"proposition_id": 1210,
"proposition": "14. Telocvik je voliteľný predmet.",
"solution": null
}
]
},
"exerciseId": 29
},
"comments": []
},
{
"id": 27,
"type": "text",
"data": "## <span id="navod">Použitie elektronického pracovného hárku\n\n### Bunky\n\nElektronický pracovný hárok je rozdelený na bunky dvoch typov – textové a aplikačné.\n\nTextové bunky obsahujú formátovaný text v značkovacom jazyku\nMarkdown (v GitHubovej verzii)\na matematické „vzorce“ v časti jazyka [ ] za [x] práve tie možnosti, ktoré sú pravdivé. Náš bakalarand pracuje na aplikácii na zjednodušenie práce s takýmito úlohami.\n\nIba :icon[tools]\n: Bunka popisuje, ako na vyriešenie úlohy použiť niektorú z aplikácií.\nAplikáciu sme buď vložili ako nasledujúcu bunku alebo si ju máte vložiť sami.\n\n:icon[write] aj :icon[tools]\n: Bunka vysvetľuje, kedy očakávame slovnú odpoveď a kedy riešenie pomocou aplikácie.\nRozhodnutie o správnom spôsobe riešenia musíte urobiť sami a následne si na riešenie vložiť vhodný typ bunky.\n",
"comments": []
}
],
"settings": {
"katexMacros": "\newcommand{\DeclareMathOperator}[2]{\newcommand{#1}{\mathop{\mathrm{#2}}}}\n\n%% General math\n\n% Domain and range\n\DeclareMathOperator{\dom}{dom}\n\DeclareMathOperator{\rng}{rng}\n\n% Powerset\n\newcommand\powerset[1]{\mathcal{P}(#1)}\n\n% Cardinality\n\newcommand{\card}[1]{\lvert#1\rvert}\n\n% Numbers\n\newcommand{\Nat}{\mathbb{N}}\n\n% Operations\n\newcommand{\TIMES}{\cdot}\n\n\n% Meta syntax %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\DeclareMathOperator{\arity}{ar}\n\newcommand{\Lang}{\mathcal{L}}\n\newcommand{\Vars}{\mathcal{V}{\Lang}}\n\newcommand{\Consts}{\mathcal{C}{\Lang}}\n\newcommand{\Preds}{\mathcal{P}{\Lang}}\n\newcommand{\Funcs}{\mathcal{F}{\Lang}}\n\newcommand{\Terms}{\mathcal{T}{\Lang}}\n\newcommand{\Atoms}{\mathcal{A}{\Lang}}\n\newcommand{\Forms}{\mathcal{E}{\Lang}}\n\newcommand{\PAtoms}{\mathcal{PA}{\Lang}}\n\newcommand{\PForms}{\mathcal{PE}{\Lang}}\n\n% Equality axioms\n\newcommand{\Eq}{\mathrm{Eq}}\n\n% Syntactic transformation\n\newcommand{\transform}{\rightsquigarrow}\n\n% Various syntactic functions\n\DeclareMathOperator{\vars}{vars}\n\DeclareMathOperator{\atoms}{atoms}\n\DeclareMathOperator{\acnt}{acnt}\n\DeclareMathOperator{\termVars}{termVars}\n\DeclareMathOperator{\free}{free}\n\DeclareMathOperator{\ground}{ground}\n\DeclareMathOperator{\mgu}{mgu}\n\DeclareMathOperator{\vcount}{vcount}\n\DeclareMathOperator{\acount}{acount}\n\DeclareMathOperator{\ccount}{ccount}\n\DeclareMathOperator{\pcount}{pcount}\n\DeclareMathOperator{\ncount}{ncount}\n\DeclareMathOperator{\cjcount}{cjcount}\n\DeclareMathOperator{\bccount}{bccount}\n\DeclareMathOperator{\lpcount}{lpcount}\n\DeclareMathOperator{\rpcount}{rpcount}\n\DeclareMathOperator{\subfs}{subfs}\n\DeclareMathOperator{\cons}{cons}\n\DeclareMathOperator{\nnf}{nnf}\n\n\n% Concrete syntax %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n% Connectives\n\n\newcommand{\nrarr}{\nrightarrow}\n\newcommand{\limpl}{\rarr}\n\newcommand{\nlimpl}{\nrarr}\n\newcommand{\lequiv}{\lrarr}\n\newcommand{\bigland}{\bigwedge}\n\newcommand{\biglor}{\bigvee}\n\newcommand{\lnand}{\mathbin{\uparrow}}\n\newcommand{\lnor}{\mathbin{\downarrow}}\n\newcommand{\lxor}{\veebar}\n\newcommand{\landnot}{\nrightarrow}\n\newcommand{\emptyclause}{\Box}\n\newcommand{\quant}[2]{\mathop{#1#2}\nolimits}\n\newcommand{\A}{\quant\forall}\n\newcommand{\E}{\quant\exists}\n\n% Symbols\n\newcommand{\sym}[1]{\text{\textsf{#1}}}\n\newcommand{\asym}[2]{\text{\textsf{#2}$^#1$}}\n\newcommand{\var}[1]{\text{\textsf{\textit{#1}}}}\n\newcommand\vk{\var{k}}\n\newcommand\vl{\var{l}}\n\newcommand\vm{\var{m}}\n\newcommand\vn{\var{n}}\n\newcommand\vo{\var{o}}\n\newcommand\vp{\var{p}}\n\newcommand\vq{\var{q}}\n\newcommand\vr{\var{r}}\n\newcommand\vs{\var{s}}\n\newcommand\vt{\var{t}}\n\newcommand\vu{\var{u}}\n\newcommand\vv{\var{v}}\n\newcommand\vw{\var{w}}\n\newcommand\vx{\var{x}}\n\newcommand\vy{\var{y}}\n\newcommand\vz{\var{z}}\n\n\n% Semantics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n% General\n\providecommand{\nmodels}\n {\mathrel{\mkern1.5mu{\not}\mkern-1.5mu}\models}\n\providecommand{\Equiv}{\mathrel{\Leftrightarrow}}\n\renewcommand{\Equiv}{\mathrel{\Leftrightarrow}}\n\newcommand{\entails}{\vDash}\n\newcommand{\nentails}{\nvDash}\n\n% Propositional\n\newcommand{\pmodels}{\models{\mathrm{p}}}\n\newcommand{\npmodels}{\nmodels_{\mathrm{p}}}\n\newcommand{\pEquiv}{\Equiv_{\mathrm{p}}}\n\newcommand{\pentails}{\entails_{\mathrm{p}}}\n\newcommand{\npentails}{\nentails_{\mathrm{p}}}\n\n% First-order\n\newcommand{\Struct}{\mathcal{M}}\n\newcommand{\InStruct}{^{\mathcal{M}}}\n\n",
"github": {
"editBranch": "tc01",
"handinBranch": ""
}
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}