For 或, what semantic notions underlie "tool or weapon on a pole" (戈) + "mouth" (口) + "territory" (1)? I consulted p 399,  ABC Chinese–English Comprehensive Dictionary (2003) that It substantiates Wiktionary's definitions. I can't access the &quot;slightly revised through July 2005&quot; ed.

How did 戈 + 口 + 1 compound to mean


or; either ... or ... (used to list alternatives)




perhaps; maybe (mostly found in news headlines)?




occasionally; sometimes


Please answer separately for each of the 3 meanings. CUHK doesn't expound. I quote Yellowbridge for completeness.

Synopsis  : 甲骨文象有納柲的「管銎斧」或「柲帽」之形，是一種兵器。後來柲形與「◎」分離，可能是變形音化，以「◎」（「員」的初文）作為「或」的聲符。
Elaboration: 甲骨文象有納柲的「管銎斧」或「柲帽」（參見下面的「其他圖片」）之形，是一種兵器。（李學勤、謝明文）商代晚期的金文與甲骨文同，後來柲形與「◎」分離。謝明文認為「◎」的脫落可能是變形音化，以「◎」（「員」的初文）作為「或」的聲符。「◎」的周圍或加上飾筆，「柲」形又演變為象「戈」形，為《說文》小篆所本。後來的人根據訛變的字體，又誤把疆域、國家之類的假借當作「或」的本義或引申義，於是把「或」附會成一個會意字，故《說文》云：「或，邦也。从囗从戈，以守一。一，地也。」
　　「或」在甲金文中多用為人名、國名或族名。如《合集》4268：「乙亥卜，永鼎（貞）：令或來歸。」季老或盉：「季老或乍（作）文考大白（伯）□□。」
　　「或」也假借作副詞，訓為「再」、「又」。如《屯南》2991+620+2291「其或幼（？）盂田」，「幼」是和祭祀有關的動詞，全句意謂在盂地之農田再一次舉行幼祭。（謝明文）[妾子]壺：「或[目又]（得）[户臣貝]（賢）[左犬]（佐）司馬賈。」
　　「或」還表示區域、疆域。如《輯佚》690+《合集》36182：「遇（?）夷方率伐東或。」表示遭逢夷方率兵攻伐東土。又如㝬鐘：「㝬其萬年，畯保四或。」黃金貴指出西周金文的「或」都讀為「域」。大西克也進一步認為春秋金文乃至郭店楚簡、楚帛書等資料中的「或」、「䧕」、「宀或」等都應讀為「域」，表示地域、領域，而不是表示國家。如《上博竹書一．緇衣》簡7：「亖（四）或（域）川（順）之。」《郭店簡．緇衣》簡12作「四方[川心]（順）之」。「四或」和「四方」都泛指天下。
There is a misunderstanding on the Wiktionary description, which shouldn't have inappropriately linked 口 and 一; these are listed for their shapes rather than their functions. The description

Ideogrammic compound (會意): 戈 + 口 + 一, “territory”.

means the separate parts which look like 戈 + 口 + 一 are combined together into one glyph to mean territory. The two meaningful components to take note of are 「戈」 (picture of a dagger-axe) and 「囗」 or 「丁」 (picture of fortifications surrounding a settlement).
Territory is now written with the derivatives

「國」 (region, country), through the addition of another semantic 「囗」
「域」 (territory, region), through the addition of semantic 「土」 (earth, soil)


西周金或作父癸方鼎集成2133
「或」 was originally a compound of 「戈」 (dagger-axe, representing military power) guarding 「囗」 or 「丁」 (picture of fortifications surrounding a settlement; see Characters&#39; original forms that have no independent usage for further discussion). The original idea was basically that of a defended settlement.
西周金保卣集成5415西周金尊集成6014西周金禹鼎集成2833
Some variants added strokes surrounding 「囗」 or 「丁」, emphasising the region's boundaries. Compare 「疆」 (originally field boundaries (畕), with lines added surrounding the fields later) or 「畫」 (to draw the line between fields (田), now written 「劃」).

Early on, 「或」 became used for a phonetic loan meaning someone, something. The meaning either, or is a semantic extension of this phonetic loan meaning. Schuessler suggests that this meaning of 「或」 (Baxter-Sagart OC: /*[ɢ]ʷˤək/) is etymologically related to 「有」 (/*[ɢ]ʷəʔ/, there is, exists). The other senses are either further semantic extensions or from compound words like

或許 (maybe)
間或 (occassionally, sometimes)