Y OU ’ RE IN THE W RONG M ARTIN A HER I NTRODUCTION D EONTICS Y OU ’ RE IN THE W RONG S OME NOTATION E NTAILMENT M ODALITY A V IOLATION - BASED C HALLENGE TO S TANDARD P UZZLES S EMANTICS FOR M ODALS R OSS ’ S PUZZLE F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS ▼❛rt✐♥ ❆❤❡r P RAGMATIC A LTERNATIVES A NDERSON ❚❛rt✉ Ü❧✐❦♦♦❧ MADRIS T HE CLAUSES D EONTICS E NTAILMENT S OLUTIONS ✶✼✳✵✺✳✷✵✶✹ F REE C HOICE ◆❛r✈❛✲❏õ❡s✉✉ D EONTIC CONFLICTS F URTHER RESEARCH
Y OU ’ RE IN THE D EONTICS W RONG M ARTIN A HER I NTRODUCTION D EONTICS S OME NOTATION E NTAILMENT M ODALITY P UZZLES D EONTIC MODALS R OSS ’ S PUZZLE F REE C HOICE K RATZER D EONTIC CONFLICTS ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ ❧❛❜♦r❛t♦r②✳ P ERMISSION : P RIOR PROPOSALS O BLIGATION : ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ ❧❛❜♦r❛t♦r②✳ P RAGMATIC A LTERNATIVES P ROHIBITION : ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ ❧❛❜♦r❛t♦r②✳ A NDERSON MADRIS T HE CLAUSES D EONTICS E NTAILMENT S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F URTHER RESEARCH
Y OU ’ RE IN THE C ONJUNCTION W RONG M ARTIN A HER I NTRODUCTION E XAMPLE : D EONTICS S OME NOTATION E NTAILMENT M ODALITY ✭✶✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧ q P UZZLES ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ R OSS ’ S PUZZLE F REE C HOICE ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P RAGMATIC T RUTH TABLE A LTERNATIVES A NDERSON MADRIS ♣ ∧ q ♣ q T HE CLAUSES D EONTICS ❚ ❚ ❚ E NTAILMENT ❚ ❋ ❋ S OLUTIONS F REE C HOICE ❋ ❚ ❋ D EONTIC CONFLICTS ❋ ❋ ❋ F URTHER RESEARCH
Y OU ’ RE IN THE C ONJUNCTION W RONG M ARTIN A HER E XAMPLE : I NTRODUCTION D EONTICS S OME NOTATION ✭✷✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧ q E NTAILMENT M ODALITY ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ P UZZLES ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q R OSS ’ S PUZZLE F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P ICTORIAL REPRESENTATION P RAGMATIC A LTERNATIVES A NDERSON ♣q MADRIS ♣q T HE CLAUSES D EONTICS E NTAILMENT S OLUTIONS ♣q ♣q F REE C HOICE D EONTIC CONFLICTS F URTHER F IGURE 1: ♣ ∧ q RESEARCH
Y OU ’ RE IN THE C ONJUNCTION W RONG M ARTIN A HER E XAMPLE : I NTRODUCTION D EONTICS S OME NOTATION ✭✸✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧ q E NTAILMENT M ODALITY ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ P UZZLES ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q R OSS ’ S PUZZLE F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P ICTORIAL REPRESENTATION P RAGMATIC A LTERNATIVES A NDERSON MADRIS ♣q ♣q T HE CLAUSES D EONTICS E NTAILMENT S OLUTIONS ♣q ♣q F REE C HOICE D EONTIC CONFLICTS F URTHER F IGURE 2: ♣ ∧ q RESEARCH
Y OU ’ RE IN THE P ICTORIAL REPRESENTATION OF ENTAILMENT W RONG M ARTIN A HER E XAMPLE I NTRODUCTION D EONTICS ✭✹✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧ q S OME NOTATION E NTAILMENT ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ M ODALITY P UZZLES ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q R OSS ’ S PUZZLE F REE C HOICE K RATZER D EONTIC CONFLICTS V IA PICTURES P RIOR PROPOSALS P RAGMATIC A LTERNATIVES A NDERSON ♣q ♣q ♣q ♣q MADRIS T HE CLAUSES D EONTICS E NTAILMENT ♣q ♣q ♣q ♣q S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F IGURE 3: ♣ ∧ q F URTHER F IGURE 4: ♣ RESEARCH
Y OU ’ RE IN THE P ICTORIAL REPRESENTATION OF ENTAILMENT W RONG M ARTIN A HER E XAMPLE I NTRODUCTION D EONTICS ✭✹✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧ q S OME NOTATION E NTAILMENT ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ M ODALITY P UZZLES ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q R OSS ’ S PUZZLE F REE C HOICE K RATZER D EONTIC CONFLICTS V IA PICTURES P RIOR PROPOSALS P RAGMATIC A LTERNATIVES A NDERSON ♣q ♣q ♣q ♣q MADRIS T HE CLAUSES D EONTICS E NTAILMENT ♣q ♣q ♣q ♣q S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F IGURE 3: ♣ ∧ q F URTHER F IGURE 4: ♣ RESEARCH
Y OU ’ RE IN THE E NTAILMENT RULE W RONG M ARTIN A HER I NTRODUCTION D EONTICS S OME NOTATION E NTAILMENT M ODALITY P UZZLES R OSS ’ S PUZZLE F REE C HOICE E NTAILMENT : K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS ✭✺✮ ϕ ❡♥t❛✐❧s ψ ✐✛ ❛❧❧ ϕ st❛t❡s ❛r❡ ❛❧s♦ ψ st❛t❡s✳ P RAGMATIC A LTERNATIVES A NDERSON MADRIS T HE CLAUSES D EONTICS E NTAILMENT S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F URTHER RESEARCH
Y OU ’ RE IN THE E NTAILMENT RULE W RONG M ARTIN A HER E QUIVALENT RULE FOR ENTAILMENT : I NTRODUCTION D EONTICS S OME NOTATION ✭✻✮ ϕ ❡♥t❛✐❧s ψ ✐✛ ❛❧❧ ¬ ψ st❛t❡s ❛r❡ ❛❧s♦ ¬ ϕ st❛t❡s✳ E NTAILMENT M ODALITY P UZZLES R OSS ’ S PUZZLE F REE C HOICE ♣ ∧ q | = ♣ K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P RAGMATIC A LTERNATIVES ♣q ♣q ♣q ♣q A NDERSON MADRIS T HE CLAUSES D EONTICS ♣q ♣q ♣q ♣q E NTAILMENT S OLUTIONS F REE C HOICE F IGURE 6: ¬ ( ♣ ∧ q ) D EONTIC CONFLICTS F IGURE 5: ¬ ♣ F URTHER RESEARCH
Y OU ’ RE IN THE E NTAILMENT RULE W RONG M ARTIN A HER E QUIVALENT RULE FOR ENTAILMENT : I NTRODUCTION D EONTICS S OME NOTATION ✭✻✮ ϕ ❡♥t❛✐❧s ψ ✐✛ ❛❧❧ ¬ ψ st❛t❡s ❛r❡ ❛❧s♦ ¬ ϕ st❛t❡s✳ E NTAILMENT M ODALITY P UZZLES R OSS ’ S PUZZLE F REE C HOICE ♣ ∧ q | = ♣ K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P RAGMATIC A LTERNATIVES ♣q ♣q ♣q ♣q A NDERSON MADRIS T HE CLAUSES D EONTICS ♣q ♣q ♣q ♣q E NTAILMENT S OLUTIONS F REE C HOICE F IGURE 6: ¬ ( ♣ ∧ q ) D EONTIC CONFLICTS F IGURE 5: ¬ ♣ F URTHER RESEARCH
Y OU ’ RE IN THE S TANDARD MODAL LOGIC W RONG M ARTIN A HER I NTRODUCTION K RIPKE MODELS D EONTICS S OME NOTATION E NTAILMENT ◮ P♦ss✐❜❧❡ ✇♦r❧❞s✿ ✭ ✇ ∈ ❲ ✮✳ M ODALITY P UZZLES ◮ ❘❡❧❛t✐♦♥s ✭ ✇❘✇ ′ ✮✳ R OSS ’ S PUZZLE F REE C HOICE ◮ ❱❛❧✉❛t✐♦♥s ✭ ✈ ∈ ❱ ✮✳ K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P RAGMATIC A LTERNATIVES A NDERSON ✇ ✵ ✇ ✶ MADRIS T HE CLAUSES D EONTICS ✇ ✷ E NTAILMENT S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F IGURE 7: ▼♦❞❡❧ ✶ F URTHER RESEARCH
Y OU ’ RE IN THE S TANDARD MODAL LOGIC W RONG M ARTIN A HER I NTRODUCTION D EONTICS E XAMPLE : S OME NOTATION E NTAILMENT M ODALITY ◮ ✈ ( ♣ , ✇ ✶ ) = ❚ P UZZLES R OSS ’ S PUZZLE ◮ ✈ ( ♣ , ✇ ✷ ) = ❋ F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P RAGMATIC ✇ ✶ A LTERNATIVES A NDERSON MADRIS T HE CLAUSES ✇ ✷ D EONTICS E NTAILMENT S OLUTIONS F IGURE 8: ❱❛❧✉❛t✐♦♥ F REE C HOICE D EONTIC CONFLICTS F URTHER RESEARCH
Y OU ’ RE IN THE S TANDARD MODAL LOGIC W RONG M ARTIN A HER Q UANTIFICATION OVER POSSIBLE WORLDS I NTRODUCTION D EONTICS ◮ ◆❡❝❡ss✐t② ✭ � ♣ ✮✿ ✉♥✐✈❡rs❛❧ q✉❛♥t✐✜❝❛t✐♦♥ S OME NOTATION ✭ ∀ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✮✳ E NTAILMENT M ODALITY ◮ P♦ss✐❜✐❧✐t② ✭ ♦ ♣ ✮✿ ❡①✐st❡♥t✐❛❧ q✉❛♥t✐✜❝❛t✐♦♥ P UZZLES R OSS ’ S PUZZLE ✭ ∃ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✮✳ F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS E XAMPLE P RAGMATIC A LTERNATIVES A NDERSON ∃ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✭✼✮ ❛✳ MADRIS ❜✳ ♦ ♣ T HE CLAUSES D EONTICS E NTAILMENT ✇ ✵ ✇ ✶ S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F URTHER ✇ ✷ RESEARCH F IGURE 9: ▼♦❞❡❧ ✶
Y OU ’ RE IN THE S TANDARD MODAL LOGIC W RONG M ARTIN A HER Q UANTIFICATION OVER POSSIBLE WORLDS I NTRODUCTION D EONTICS ◮ ◆❡❝❡ss✐t② ✭ � ♣ ✮✿ ✉♥✐✈❡rs❛❧ q✉❛♥t✐✜❝❛t✐♦♥ S OME NOTATION ✭ ∀ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✮✳ E NTAILMENT M ODALITY ◮ P♦ss✐❜✐❧✐t② ✭ ♦ ♣ ✮✿ ❡①✐st❡♥t✐❛❧ q✉❛♥t✐✜❝❛t✐♦♥ P UZZLES R OSS ’ S PUZZLE ✭ ∃ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✮✳ F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS E XAMPLE P RAGMATIC A LTERNATIVES A NDERSON ∃ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✭✼✮ ❛✳ MADRIS ❜✳ ♦ ♣ T HE CLAUSES D EONTICS E NTAILMENT ✇ ✵ ✇ ✶ S OLUTIONS F REE C HOICE D EONTIC CONFLICTS F URTHER ✇ ✷ RESEARCH F IGURE 9: ▼♦❞❡❧ ✶
Y OU ’ RE IN THE S TANDARD MODAL LOGIC W RONG M ARTIN A HER I NTRODUCTION D EONTICS E XAMPLE S OME NOTATION E NTAILMENT M ODALITY ∀ ✇ : ✇ ′ ❘✇ : ✇ ∈ ♣ ✭✽✮ ❛✳ P UZZLES R OSS ’ S PUZZLE ❜✳ � ♣ F REE C HOICE K RATZER D EONTIC CONFLICTS P RIOR PROPOSALS P RAGMATIC ✇ ✵ ✇ ✶ A LTERNATIVES A NDERSON MADRIS T HE CLAUSES ✇ ✷ D EONTICS E NTAILMENT S OLUTIONS F IGURE 10: ▼♦❞❡❧ ✶ F REE C HOICE D EONTIC CONFLICTS F URTHER RESEARCH
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