This page is the actual full page of serious references. If you are looking for just a few systems but lots of flashy diagrams, you want http://www.cc.utah.edu/~nahaj/logic/structures/ which also gives an explaination of notations used and other housekeeping information.

This started as a list of Modal Logic systems I encountered. In the end it is a list of mostly modal logic systems. (But even at that, the list has grown LARGE.) Dr. Peter Suber has a list of the types of logics that covers the various types. It provides a bibliography of the various kinds of logics for a much wider class of logics than I cover, but no cross references of alternate names, and few individual representitives.

This list documents the fact that many systems have been investigated under different names, and that some names have historically been applied to several different systems. I'm not aware of any other such cross reference on the net (or anywhere else). If you are aware of such a reference, please drop me a line.

Jump to systems starting with: 0-9 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

- Jump to start of systems
- Jump to Georgacarakos' "J" systems
- Jump to Lewis' "S" systems
- Sobociński's "K" sytems
- Sobociński's "Z" systems
- Bibliography

- 0p is called the Trivial System
- "10 modalities calculus" (Becker) =[Parry, 1953, p150]= S5 (Lewis)
- 2' (Feys) =[Feys, 1965, p123]= T (Feys)
- 2r (Pledger) =[Pledger 1972 p270]= S5 (Lewis)
- 3q (Pledger) =[Pledger, 1972, p270]= K2 (Sobociński)
- 4q (Pledger) =[Pledger, 1972, p270]= K1 (Sobociński) =[Pledger, 1972, p270]= S4.1 (McKinsey) = [Pledger, 1972, p270]= S4M
- 4s =[Pledger, 1972, p270]= S4.2 (P.T. Geach)
- 6p (Pledger)
- 6s (Pledger) = ([Pledger, 1972, 271]) S4 (Lewis)
- 8p (Pledger)
- 8pa (Pledger) =[Pledger 1972, p279]= 8pc (Pledger) =[Pledger 1972, p279]= S9 (Hughes and Cresswell)
- 8pb (Pledger) = 8pc =[Pledger 1972, p279]= S9 (Hughes and Cresswell)
- 8pc (Pledger) =[Pledger 1972, p279]= S9 (Hughes and Cresswell)

- 8q (Pledger)
- 10p (Pledger)
- 10pa (Pledger) reduces to 10pb (Pledger)
- 10pb (Pledger)
- 10pc (Pledger) = S8 (Alban) [Pledger, 1972, 271]

- 10r (Pledger)
- 12p (Pledger)
- 12pa (Pledger)
- 12pb (Pledger)
- 12pc (Pledger) reduces to 10pc (Pledger) = S8 (Alban)

- 12q (Pledger)
- 12qa (Pledger) reduces to 12qb (Pledger)
- 12qb (Pledger)
- 12qc (Pledger) reduces to 10pc (Pledger) = S8 (Alban)

- 12r (Pledger) = S3.5 (Åqvist)
[Pledger,
1972, 271]
- 12ra (Pledger) reduces to 8pc =[Pledger 1972, p279]= S9 (Hughes and Cresswell)
- 12rb (Pledger) reduces to 8pc =[Pledger 1972, p279]= S9 (Hughes and Cresswell)
- 12rc (Pledger) reduces to 8pc =[Pledger 1972, p279]= S9 (Hughes and Cresswell)

- 12s (Pledger)
- 14q (Pledger)
- 14qa (Pledger)
- 14qb (Pledger)
- 14qc (Pledger) reduces to 10pc (Pledger) = S8 (Alban)

- 14r (Pledger)
- 14ra reduces to 14rb (Pledger)
- 14rb (Pledger)
- 14rc reduces to 10pc (Pledger) = S8 (Alban)

- 16s (Pledger)
=[Sobociński,
1976a]=
S3.01 (Sobociński)
- 16sa (Pledger) reduces to 16sb (Pledger)
- 16sb (Pledger)
- 16sc (Pledger) reduces to 10pc (Pledger) = S8 (Alban)

- 18r (Pledger)
- 18ra (Pledger)
- 18rb (Pledger)
- 18rc reduces to 10pc (Pledger) = S8 (Alban)

- 20s (Pledger)
=[Pledger,
1972, 271]=
S3 (Lewis)
- 20sa (Pledger) =[Pledger, 1972, 277]= S7 (Halldén)
- 20sb (Pledger) =[Pledger, 1972, 277-fn4]= S7.5 (Anderson)
- 20sc (Pledger) reduces to 10pc (Pledger) = S8 (Alban)

- Aristotle (Αριστοτἑλης)

- B (Brouwer) =[Chellas 1980, p131]= KTB =[Priest, 2001, p39]= = Kρσ
- B (Moh Shaw-Kwei) [Feys,
1965,
p139] (Quoting [Shaw-Kwei, 1958] "
*Modal systems with a finite number of Modalities*" in the Journal*Scientia Sinica*#7, p388-412)- B
_{1}(Moh Shaw-Kwei) - B
_{2}(Moh Shaw-Kwei) - B
_{3}(Moh Shaw-Kwei) - ... B
_{n}(Moh Shaw-Kwei) ... Infinite number of systems.

- B
- BCI (Meredith)
- BCK (Meredith)
- BCSK (Spinks) (Humberstone)
**[Humberstone, 2000]**

- C disambiguation
- C (Chellas) [Priest, 2001, p74]
- CLC (Bull) - implicational fragment of
Dummett's LC
**[Bull, 1962]** - CH (Bull) - implicational fragment of Heyting's Calculus [Bull, 1962]
- C1 - Strict implicational fragment of S1
- C2 - Strict implicational fragment of S2
- C3 (Hacking) - Strict implicational fragment of S3
- C4 (Anderson and Belnap) - Strict implicational
fragment of S4
Also (Hacking)
- ?? - Strict implicational fragment of S4
^{0}(Zeman) [Zeman 1979, NDJFL]

- ?? - Strict implicational fragment of S4
- C5 - Strict implicational fragment of S5 (Lewis)
- CT (Hacking) - Strict implicational fragment of T (Feys)
- ?? (Zeman)- Strict implicational fragment of T
^{0}**[Zeman 1979, NDJFL]**

- ?? (Zeman)- Strict implicational fragment of T
- CM - Strict implicational fragment of M

*D Disambiguation*

- D (Lemmon and Scott) = KD [Chellas, 1980, p131] = Kη [Priest, 2001, p39]
- D (Prior) = [Zeman, 1973, p245]= S4.3.1 (Sobociński)

Systems:

- D1 (Lemmon)
- D2
- D2 (Lemmon)
- D2 (Jaskowski)

- D3 (Lemmon)
- D4
- D4 (Lemmon)
- D4 (D+4)

- D45 (D+4+5)
- D5
- D5 (Lemmon)
- D5 (D+5)

*Deontic (or Deontik) Disambiguation*

- Deontic ("Standard")
- Deontic (von Wright, 1951)
- Deontic (von Wright, 1956)
- Deontic (von Wright, 1965)
- Deontik (Mally)

*E disambiguation The System E can be:*- E = Equivalence Logic
- E (Anderson and Belnap) [Anderson and Belnap, 1962]
- E
_{1}(Anderson and Belnap) [Anderson and Belnap, 1962] - E (Challas and others) Used to form:
- E (H.B. Smith) [not named by Smith, but later by the late C. West. Churchman's "Towards a general logic of propositions"]

- E1 (Lemmon)
- E2 (Lemmon)
- E3 (Lemmon)
- E4 (Lemmon)
- E5 (Lemmon)
- E6
- E7
- EM (Challas) = M [Chellas, 1980, p237]
- EMN
- EN
- EV
**[von Wright, 1951, p42]**(Where he also creates system VE) - E+ [Hughes and Cresswell, 1996, p364]

- G (Boolos) = KW (Segerberg)
[Hughes & Cresswell,
1996, p139]
= K4W [Boolos, 1993, p272
(index entry)]
= PrL [Boolos, 1993, p272
(index entry)]
= GL [Boolos, 1993, xvi]
- Boolos' GL is the same as KW (Segerberg) [Boolos, 1993, p272 (index entry)] [Boolos, 1993, xvi]

*H Disambiguation*

- H (For Henkin) [Boolos, 1993, p149]
- H (For Heyting) [McKinsey and Tarski, 1948]

Systems

- HIC ("Heyting's Intuitionist Calculus")
- HPC ("Heyting's Predicate Calculus") [Kreisel, JSL, 1962, p139]

- I [Kripke, 1963]
- ICI (Intuitionist Calculus of Implication) is also called PIC (Positive Implicational Calculus) [Zeman, 1973]
- IIC "Implications fragment of the Intuitionist Calculus" [Bull, 1962]
- Inconsistent Systems
- Intuitionist PC
- IS4 (Intuionist S4) <-- On an Intuitionistic Modal Logic [Studia Logica, Vol. 65, No. 3 (Aug., 2000), pp. 383-416] -->
- I4
^{0}(Zeman) - IQ (Zeman) ["Implicit quantification"]
- IT
^{0}(Zeman)

- J (Brown) [Brown, 1982, NDJFL]
- J systems of Georgacarakos
(Note that Pledger points out
[Pledger,
1980, pg683]
that Georgacarakos' J1 - J3 are three representitives of a much larger
family of logics. -JH)
- J1 (Georgacarakos)
- J2 (Georgacarakos)
- J3 (Georgacarakos) = 8p (Pledger) [Pledger, 1980, p 683]

- Johansson's Minimal Calculus (Johansson)

- K (Segerberg)
[Also called RN, MCN, EMCN]
- KC [Chagrov and Zakharyaschev, 1997]
- KF (Lemmon) [Lemmon and Scott, 1977]
- KH
- Kρ = T (Feys) [Priest, 2001, p39]
- Kρσ = B (Brower) [Priest, 2001, p39]
- Kρη = D (Lemmon) [Priest, 2001, p39]
- Kρτ = S4 (Lewis) [Priest, 2001, p39]
- Kρστ = S5 (Lewis) [Priest, 2001, p39]
- KT5 (K+T+5) =[Chellas, 1980, p139]= S5(Lewis)
- KW (Segerberg) = G (Boolos) [Hughes & Cresswell, 1996, p139] = GL (Boolos) [Boolos, 1993, xvi], = K4W [Boolos, 1993, p272 (index entry)] = PrL [Boolos, 1993, p272 (index entry)])
- K
_{T}(Lemmon) - K
_{B} - K
_{L}

- K1 (Sobociński) = S4M
[Pledger, 1972, p270]
= S4.1 (McKinsey)
[Hughes and Cresswell,
1996, p143 (Ch 7, fn7)]
= 4q (Pledger)
[Pledger,
1972, p270]
- K1.1 (Sobociński)
- K1.1.5

- K1.2 (Sobociński)

- K1.1 (Sobociński)
- K2 (Sobociński)
- K2.1 (Sobociński)

- K3 (Sobociński)
*K4 disambiguation page*- K4 formed by
system K
+ axiom Lp > LLp
- KD4
- K4W = KW (Segerberg) = G [Hughes and Cresswell, 1996, p139] = GL [Boolos, 1993, xvi] = PrL [Boolos, 1993, p272 (index entry)])
- K4Z

- K4 (Sobociński) formed
from system S4.4 plus the axiom
LMp=>MLp
- K4.1
- K4.2
- K4.2.1
- K4.2Z
- K4.2W

- K4.3
- K4.3.1
- K4.3W
- K4.3Z

- K4 formed by
system K
+ axiom Lp > LLp
- K5 (Sobociński)
- KE
- KTB = B [Chellas, 1980, p131]

*L Disambiguation*

- L (Curry) [Mentioned in Feys, 1965]
- L (Emch) [Emch, 1936]
- L (Church) [Church, 1936]
- Ł (Łukasiewicz) [Smiley, NDJFL, 1961]
- Ł
_{ℵ}(Łukasiewicz) [Priest, 2001, 217-218]

- Ł
- L (Kohn) [Kohn, 1977, NDJFL]

Systems

- LA (?) [Curry, 1952, JSL V17 #2 (1952), p98-104]
- LC (Dummett) [Dummett, 1959]
- LD (Johansson) [Curry, 1952, JSL, v17, #1 (1952), 35-42]
- LFX (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]
- LIC (Bull)
**[Bull, 1962]** - LJ (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]
- LK (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]
- LKY (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]

- LL (for Lewis and Langford) is a common late 1930's term for system S (Lewis) which was eventually called S3 (Lewis)
- LM (Curry) [Curry, 1952, JSL V17 #2, p98-104]
- LMF (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]
- LM* (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]

- LX (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]
- LXF (Curry) [Curry, 1952, JSL V17 #2 (1952), p98-104]

*M Disambiguation*

- M (von Wright) is T (Feys) [Hughes & Cresswell, 1968, p125]
- M (Chellas) = EM [Chellas, 1980, p237]
- M (Megill and Bunder) [Megill and Bunder, 1996]

Systems:

- MIPQ (Prior) [Prior, 1957 Time and modality.] [Bull 1964, p142]
- The Marked system (Lp == Mp) (Halleck) is KF (Lemmon)
- M' (von Wright) [von Wright, 1951, p84-85] is S4 (Lewis)
- M'' (von Wright) [von Wright, 1951, p84-85]
- M
_{1}[von Wright, 1951, p8] - M
_{2}[von Wright, 1951, p57]

- N [Vredenduin, 1939]
- νSa (Porte) [Feys, 1965, p142]
- νSb (Porte) = νSc (Porte) [Feys, 1965, p142]
- νSc (Porte) = νSb (Porte) Feys, 1965, p142]

*P*_{+}disambiguation

- P1 (Lemmon) = S1 (Lewis) [Lemmon, 1957, p178]
- P2 (Lemmon) = S2 (Lewis) [Lemmon, 1957, p178]
- P3 (Lemmon) = S3 (Lewis) [Lemmon, 1957, p178]
- P4 (Lemmon) = S4 (Lewis) [Lemmon, 1957, p178]
- P5 (Lemmon) = S5 (Lewis) [Lemmon, 1957, p178]
- PIC (Positive Implicational Calculus) = ICI
- PC ("Standard")
- PC (Intuitionist)
- PCI The pure implicational fragment of PC
- Prl = KW (Segerberg) = G (Boolos) [Hughes and Cresswell, 1996, p139] = GL [Boolos, 1993, xvi], = K4W [Boolos, 1993, p272 (index entry)]
- Positive Propositional Logic (PPL)
- PPL (Hilbert)
= P
_{+}(Hackstaff) [Hackstaff, 1966, p50] - PPL (Church) [Hackstaff, 1966, p50 footnote]

- PPL (Hilbert)
= P
- P-W (Anderson and Belnap) [Anderson and Belnap, "
*Entailment*"]

- Q (Prior) [Hughes and Cresswell, 1968, p303-305]
- QML (Barcan)

- R = EMC [Chellas, 1980, p237]
- R* (Routley) [NDJFL, Vol 7 (1966), pg 251-276]
- +R* (Routley) [NDJFL, Vol 11, #3, 1970, page 295]
- R1 (Canty)
[Canty,
1965a]
- R1 (Canty)
- R1
^{0}(Canty) - R1* (Canty)

- R2 (Canty)
[Canty,
1965a]
- R2 (Canty)
- R2
^{0}(Canty) - R2* (Canty)

- R3 (Canty) = S3 (Lewis)
[Canty,
1965a, p317]
- R3
^{0}= S3^{0}(Sobociński) [Canty, 1965a, p317] - R3* = S3* (Sobociński) [Canty, 1965a, p314]

- R3
- RW = C (Chellas) [Priest, 2001, p74]
- ρSa (Porte) = ρSb (Porte) [Feys, 1965, p143]
- ρSb (Porte) = ρSa (Porte) [Feys, 1965, p143]
- ρSc (Porte) [Feys, 1965, p143]

- S disambiguation
- S0 (Halldén) [Halldén, 1948]
(As quoted by [Feys,
1965, p139],
quoting Halldén's paper in "
*Theoria*", Volume 14, p265-269)- S0.5 (Lemmon)
[Lemmon
1957, p181]
- S0.5
^{0}

- S0.5
- S0.9 (Lemmon)
[Lemmon
1957, p180]
- S0.9
^{0}

- S0.9

- S0.5 (Lemmon)
[Lemmon
1957, p181]
- S.1 (Parry) Mentioned by [Lemmon 1957, p181fn]
- S1 (Lewis)
- S1
^{0}(Feys) [Sobociński, 1962, p53]

- S1
- S2 (Lewis)
- S2
^{0}(Feys) [Sobociński, 1962, p53] - S2' (Feys) is T [Feys, 1965, p123]

- S2
- S3 (Lewis) = 20s
[Pledger, 1972, p271]
[ And historicly, S3 (Lewis) = S (Lewis)
= LL (Lewis and Langford), see the S (Lewis) page for details. ]
- S'3 (Moh Shaw-Kwei) [Feys, 1965, p140,139]
- S3* (Sobociński)
**[Sobociński, 1962, p53]**= R1* (Canty) [Canty, 1965a, p317]- S3** (Thomas)
**[Thomas, 1973, NDJFL]**

- S3** (Thomas)
- S3
^{0}(Sobociński)**[Sobociński, 1962, p53]**= R1^{0}(Canty) [Canty, 1965a, p317] - S3.01 (Sobociński) is 16s (Pledger) [Sobociński, 1976a]
- S3.02 (Sobocinski) = S3.03 (Sobociński)
[Schumm,
1974]
- S3.02
^{0}(Sobociński)**[Sobociński, 1976a]**

- S3.02
- S3.03 (Sobociński) [Pledger, 1975, pg.271]
- S3.03
^{0}(Sobociński)**[Sobociński, 1976a]**

- S3.03
- S3.04 (Sobociński)
[Pledger,
1975, pg.271]
- S3.04
^{0}(Sobociński)**[Sobociński, 1976a]**

- S3.04
- S3.3 (Hughes & Cresswell) [Hughes & Cresswell, 1968, 265] is actually S3.5 (Åqvist). [Pledger, 1972, sec 6, p276] [Pledger, 2000]
- S3.5 (Åqvist) = 12r (Pledger) [Pledger, 1972, p271]
- S3(S) (Lemmon) = S3.5 (Åqvist) = 12r (Pledger) [Pledger 2000] [Rennie, 1968 (JSL), p444]

- S4 (Lewis) = KT4 = 6s (Pledger)
[Pledger, 1972, p271]
= Kρτ
[Priest,
2001, p39]
= νρSc (Porte)
[Feys,
1965,
p144]
- S4* (Kanger) = S4 (Lewis) [Feys, 1965, p178-185] [Hughes and Cresswell, 1996, p344]
- S4* (Onishi and Matsumoto) = S4 (Lewis) [Feys, 1965, p176-178]
- S4
^{0}(Sobociński)**[Sobociński, 1962, p53]** - S4.01 [Goldblatt, 1973a]
- S4.02 (Sobociński)
**[Sobociński, 1971]** - S4.03 (Georgacarakos) = S4.03 (Lenzen) [Lenzen, 1978, p249] !!!
- S4.04 (Zeman)
- S4.05
- S4.1 (Sobociński)
*S4.1 Disambiguation*- S4.1 (Sobociński)
- S4.1 (McKinsey) = S4M [Hughes and Cresswell, 1996, p143, fn7]

- S4.1.1 = S4.1 [Sobociński, NDJL, 1971, p372]
- S4.1.2 (Sobociński) = S4.1.3 [Sobociński, NDJL, 1971, 372]
- S4.1.3 = S4.1.2 [Sobociński, NDJL, 1971, 372]

- S4.2 (P.T. Geach)
- S4.3 [Dummett and Lemmon, 1959]
- S4.3.1 (Sobociński) is
([Zeman,
1973, p245]
[Hughes and Cresswell,
1994, p180])
D (Prior)
**[Prior, 1967, p29]** - S4.3.2
- S4.3.3 (Zeman) =[Sobociński, NDJL, 1971, 372]= S4.1.3 =[Sobociński, NDJL, 1971, p373]= Z7 (Sobociński)
- S4.3.4 (Zeman) =[Sobociński, NDJL, 1971, p373]= Z8 (Sobociński)

- S4.3.1 (Sobociński) is
([Zeman,
1973, p245]
[Hughes and Cresswell,
1994, p180])
D (Prior)
- S4.4 (Sobociński)
- S4.5 (Parry) =[Sobociński 1964, p74] [Hughes and Cresswell, 1968, p264] [Zeman, 1973, p230]= S5 (Lewis)
- S4.6 = S4.9 (Schumm) [Zeman, NDJFL, 1972, p118]
- S4.7 (Schumm) is S4.9 (Schumm) [Zeman, 1973, p266]
- S4.9 (Schumm)
- S4F
- S4M
=[Hughes and Cresswell,
1996, p143, fn7]=
S4.1 (McKinsey)
- S4M1 [Hughes and Cresswell, 1996, p132]

- S5 (Lewis)
=[Pledger,
1972, p270]=
2r (Pledger)
=[Priest,
2001, p39]=
Kρστ
=[Chellas,
1980, p139]=
KT5
=[Hughes and Cresswell,
1996, p344 B]=
S5* (Kanger). Not to be confused with S5-UC.
- S5* (Kanger) = ([Hughes and Cresswell, 1996, p344 B]) S5 (Lewis)
- S5
^{0}=[Zeman, 1973, p181]= S5 (Lewis) - S5-UC (S5, universally quantified)
- S52R* (Routley) [NDJFL, Vol 11, #3, 1970, page 294]
- +S52R* (Routley) [NDJFL, Vol 11, #3, 1970, page 290] [A second order modal logic - JH]

- S6 (Alban)
- S7 (Halldén)
=[Pledger
1972, p277]=
20sa (Pledger)
- S7
^{0} *S7.5 disambiguation*- S7.5 (Anderson) = 20sb (Pledger) [Pledger, 1972, p277-fn4]
- S7.5 (Åqvist) = 8pc (Pledger) [Pledger, 1972, p277-fn4] which is S9 (Hughes and Cresswell) [Hughes & Cresswell, 1968, p272-fn301] Which is called S8.5 by Cresswell in [Cresswell, 1967, p59, bottom].

- S7
- S8 (Alban) = 10pc (Pledger)
[Pledger, 1972, p278]
- S8.1 (McCall and Nat) =[Pledger, 1972, p280-para2]= 8pc (Pledger) =[Hughes and Cresswell, 1968, p272-fn301]= S9 (Hughes and Cresswell)
- S8.1 (Åqvist) =[Hughes and Cresswell, 1968, p272-fn301]= S9 (Hughes and Cresswell)
- S8.5 appearing in [Cresswell, 1967] is also 8pc (Pledger) [Pledger, 1972, p280-para2] = S9 (Hughes and Cresswell) [Hughes and Cresswell, 1968, p272-fn301]

- S9 (Hughes and Cresswell) [Hughes & Cresswell, 1968, p272-fn301]
- Sa (Porte) [Feys, 1965, p141]
- Sb (Porte) [Feys, 1965, p141]
- Sc (Porte) [Feys, 1965, p141]

- T (Feys) =
KT
=[Hughes and Cresswell,
1968, p125]=
M (von Wright)
=[Lemmon
1957, p179]=
T (Gödel)
=[Priest,
2001, p39]=
Kρ
=[Feys,
1965, p123]=
2' (Feys), or S2' (Feys)
- T
^{0}(Thomas) - T
^{x}(Sobociński) - T.0.4 (Zeman) [Zeman 1969 NDJFL]
- T.2 (Zeman) [Zeman 1969 NDJFL]
- T.4 (Zeman) [Zeman 1969 NDJFL]

- T
- "Ten modalities calculus" (Becker) =[Parry, 1953, p150]= S5 (Lewis)
- TRC (Holmes) [Thomas Jech, JSL Vol 64, #4, 1999, pp1811-1819]
- TRCL (Holmes) [Thomas Jech, JSL Vol 64, #4, 1999, pp1811-1819]
- The Trivial system (Lp == p == Mp)

- Ul

- V1 (Sobociński)
**[Sobociński, 1970]** - V2 (Sobociński)
**[Sobociński, 1970]** - VE
**[von Wright, 1951, p42]**(Where he also creates system EV) - The VER Verum system (Lp)

- Z1 (Sobociński)
**[Sobociński, 1971a, p371]**- Z1.5

- Z2 (Sobociński)
**[Sobociński, 1971a, p371]** - Z3 (Sobociński)
**[Sobociński, 1971a, p371]** - Z4 (Sobociński)
**[Sobociński, 1971a, p371]** - Z5 (Sobociński)
**[Sobociński, 1971a, p371]** - Z6 (Sobociński)
**[Sobociński, 1971a, p371]** - Z7 (Sobociński)
**[Sobociński, 1971a, p371]**= S4.3.3 (Zeman) - Z8 (Sobociński)
**[Sobociński, 1971a, p371]**= S4.3.4 (Zeman) - Z9 (Sobociński)
**[Sobociński, 1971a, p371]**=[Sobociński, 1971a, p371]= S4.6 (Zeman) =[Zeman, 1972, p118, towards end.]= S4.9 (Schumm)

- Systems originally added (many years ago) don't have, and do need, references more like the more modern ones have.
- In cases where two axiomatizations of the same system have different extensions when a new axiom is added, these pages may have them with the same extension. Some of the cases I can blame on the original quoted authors, some are my own sloppyness. I'm working to get these fixed. (Thanks to Petr Pudlák for reminding me of the issue.)(Hughes and Cresswell cover the issue in passing several times.)
- I need to be more careful about noting which ones were originally presented as axiom schemata, but are presented as axioms here.
- I need to hunt down more original sources, so that presentations can be made to agree with those sources. (Since, for example, Hughes and Cresswell present axioms even in cases where the original was in terms of axiom schemata.)
- I am aware of maybe twice as many named logics than appear on these pages. And I seem to be always finding new ones. And new ones are being published all the time. There will always be something to do.
- A number of mappings between paraconsistent, relevant, and modal logics have recently been brought to my attention. The containment questions have expanded greatly.
- Some early pages seem to have some confusion between the purely implicational fragment of a system and the system formed by using only the system's axioms for implication.

Large numbers of researchers have "pet problems" about some particular system they are working on. These include those looking for decision procedures (or proof there isn't one), completeness (or proof it isn't complete), etc. I've added a "Community Requests" section to some pages where specific questions about the system and who's looking for an answer.

If you are a researcher, and you want such a note added for a system you are working on, please contact John.Halleck@utah.edu .

- Individual Axioms Pages
- Rules page
- Bibliography
- Logic Structures Page
- Logic Page
- John Halleck's Home Page

© Copyright 2007,2009 by John Halleck, All Rights Reserved. This page is http://www.cc.utah.edu/~nahaj/logic/structures/systems/index.html This page was last modified on Wednesday, October 9th, 2013.