SYSTEM://logic.quest
--:--:-- UTC
// SESSION 0x4F.A1 // PROTOCOL: TRUTH // LAYER: 00
[ READY ] PUZZLES: 184 SOLVED: 09127

logic.quest _

[ a logical reasoning operating system ]

$ scroll --depth=increase
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// MANIFEST.LOG 0x01
┌────────────────────────────────────────────────────────────────────────┐
│  PROTOCOL  :  TRUTH-EVAL                                               │
│  VERSION   :  4.7.2                                                    │
│  AUTHORITY :  THE OBSERVER                                             │
│  STATUS    :  ACTIVE                                                  │
└────────────────────────────────────────────────────────────────────────┘

logic.quest is not a game. it is a deduction engine -- a sealed environment where premises are inputs, conclusions are outputs, and every step between is a gate to be traversed. you will learn to read the wiring of an argument. you will learn to feel a contradiction before you see it. you will descend.

each puzzle compiles. each solution propagates. each error halts the system. truth is not opinion -- truth is whatever survives the truth table.

SYLLOGISMS

// AND-GATE :: both premises must hold
D-01
// PREMISE.STACK P.01
  • All logicians are mortal.
  • Aristotle is a logician.
  • ∴ Aristotle is mortal.
P → Q && Q → R P → R
// TRUTH.TABLE T.AND
ABA && B
TTT
TFF
FTF
FFF
// VENN.DIAGRAM V.AB

intersection ≡ conjunction ≡ truth held in common

TRUTH TABLES

// OR-GATE :: at least one input asserts
D-02
// EVAL :: P ∨ Q ∨ ¬R E.03
PQR¬RP ∨ Q(P ∨ Q) ∨ ¬R
TTTFTT
TFTFTT
FTFTTT
FFTFFF
FFFTFT
// LEGEND L.00
  • TRUE  :: assertion holds
  • FALSE  :: contradiction
  • UNKNOWN :: pending eval
┌───┬───┬─────┐
│ P │ Q │ P∨Q │
├───┼───┼─────┤
│ T │ F │  T  │
└───┴───┴─────┘

PARADOXES

// NOT-GATE :: inversion at the boundary
D-03
// LIAR.PARADOX X.01
" this statement is false. "
  • if TRUE → it is FALSE → contradiction.
  • if FALSE → it is TRUE → contradiction.
L ≡ ¬L ⊥ HALT
// RUSSELL.SET X.02

R = { x | x ∉ x }
does R contain itself?

  • R ∈ R → R ∉ R
  • R ∉ R → R ∈ R
// SHIP.OF.THESEUS X.03

replace plank₁. is the ship the same?
replace plank₂...n. when does identity break?

∀n: ship(t) ≈ ship(t+1) ?

DEDUCTION

// XOR-GATE :: exactly one signal asserts
D-04
// CASE.FILE :: WHO BROKE THE GATE? C.07
  • there are 3 suspects: A, B, C. exactly one is guilty.
  • A says: "B did it."
  • B says: "i did not do it."
  • C says: "A is lying."
  • exactly one of them tells the truth.

$ tap a suspect to evaluate the propagation...

// XOR.TABLE T.XOR
ABA ⊕ B
TTF
TFT
FTT
FFF

SYSTEM

// LIVE.METRICS :: from the deduction engine
D-05
// PUZZLES.ACTIVE 000
// SOLVERS.ONLINE 0000
// PROOFS.VERIFIED 00000
// PARADOX.DEPTH.MAX 00
┌─────────────────────────────────────────────────────────────────────┐
│  ENTRY POINT  ::  authentication required                           │
│  PROTOCOL     ::  truth-eval 4.7.2                                  │
│  WARNING      ::  descent is non-reversible                          │
└─────────────────────────────────────────────────────────────────────┘

JACK IN

[ solve to descend. each layer is a gate. each gate is a truth. ]

00:00.001OKterminal awake
00:00.014OKtruth-table cache primed
00:00.027OK184 puzzles loaded
00:00.041--3 paradoxes unresolvable (expected)
00:00.058OKawaiting operator...