O ganon F 30 (1) 2023: 66–101 ISSN 2585-7150 (online)
h ps://doi.o g/10.31577/o g .2023.30105 ISSN 1335-0668 (p in )
* VSB-Technical Uni e si y o Os a a
h ps://o cid.o g/0000-0002-5393-6916
 Depa men o Compu e Science FEI, VSB-Technical Uni e si y o Os a a,
Czech Republic
 ma [email protected]
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RESEARCH ARTICLE
Speci ica ion o Agen s’ Ac i i ies in Pas ,
P esen and Fu u e
Ma ie Duží*
Recei ed: 5 Sep embe 2022 / Re ised: 11 No embe 2022 / Accep ed: 9 Decembe 2022
Abs ac : The beha iou o a mul i-agen sys em is d i en by mes-
saging. Usually, he e is no cen al dispa che and each au onomous
agen , hough esou ce-bounded, can make less o mo e a ional de-
cisions o mee i s own and collec i e goals. To his end, howe e ,
agen s mus communica e wi h hei ellow agen s and accoun o
he signals om hei en i onmen . Mo eo e , in he dynamic, pe -
manen ly changing wo ld, agen s’ beha iou , i.e. hei ac i i ies,
mus also be dynamic. By communica ing wi h o he ellow agen s
and wi h hei en i onmen , agen s should be able o lea n new con-
cep s and en ich hei knowledge base. P ocesses and e en s ha
happened in he pas may be i ele an in he p esen o ha e a
signi ican impac in he u u e, and ice e sa. The e o e, he ine-
g ained analysis o agen s’ ac i i ies as well as e en s wi hin o be-
yond he sys em is e y impo an so ha he sys em can un
smoo hly wi hou alling in o inconsis encies. Mo eo e , as he sys-
em should communica e wi h i s en i onmen , he analysis should
be as close o na u al language as possible. The goal o his pape is
a p oposal o such an analysis. To his end, I apply T anspa en
In ensional Logic (TIL) because TIL is pa icula ly ap o a ine-
g ained analysis o p ocesses and e en s speci ied in he p esen , pas
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 67
O ganon F 30 (1) 2023: 66–101
o u u e ense wi h e e ence o he ime when hey happened, hap-
pen o will happen.
Keywo ds: Ac i i y; Communica ion o agen s; T anspa en In en-
sional Logic; Na u al language p ocessing; Sen ences in di e en
enses.
1.
In oduc ion
A mul i-agen sys em (MAS) is a dis ibu ed sys em o (mo e o less)
in elligen agen s who a e ac i e in hei pe cei ing en i onmen and ac ing
o achie e hei indi idual and collec i e goals.1 The agen s a e au onomous
in he sense o no being con olled by a cen al dispa che ; he sys em is
d i en only by messaging.2 To ob ain a needed piece o in o ma ion, he
agen s mus be able o ask hei ellow agen s. Ye , hey need o pu o wa d
no only Yes-No ques ions bu also, in pa icula , Wh-ques ions. While
he e is jus one ype o answe o a Yes-no ques ion, he class o Wh-
ques ions is much mo e abundan in ypes. F om he logical poin o iew,
he ype o possible answe de e mines he ype o Wh-ques ion. In egula
communica ion, we ask by using di e en p onouns in in e oga i e sen-
ences, and hese p onouns indica e he ype o possible answe . We can
in eg a e logical and linguis ic iews o classi y Wh-ques ions in o mo e
de ailed classes. Fo ins ance, by ‘who’, we ask o a pe son; by ‘whe e’, o
a loca ion o posi ion; ‘when’ means asking o he ime. A p oposal o such
a mo e de ailed classi ica ion o Wh-ques ions has been in oduced in
(Číhalo á, Duží 2022). Each specialised sub ype o a Wh-ques ion con eys
speci ic ins uc ions o an agen on how and whe e o ind he co espond-
ing answe . De ailed classi ica ion o que ies hus imp o es agen s’ commu-
nica ion and in elligen beha iou . In pa icula , he speci ic ypes o Wh-
ques ions a e ap o he communica ion o agen s conce ning hei dynamic
1 By ‘in elligen ’ I do no mean human in elligence in case o so wa e agen s, o
cou se. Ins ead, I am alking abou a i icial in elligence, which is ac ually no an
in elligence, as Roge Pen ose in his 1994 book a gues. Anyway, in his pape I use
he e m ‘in elligence’ o bo h.
2 See, o ins ance Woold ige (2009).
68 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
ac i i ies. The agen s need o know who is he ac o o an ac i i y, when
he ac i i y s a s and ends, by which ins umen s i is pe o med, e c.
The sys ems o e o e ic logic a e aluable, as hey ende many exci ing
ea u es o Yes-No ques ions and answe s.3 Howe e , many o he essen ial
ea u es o ques ions s em om hei p esupposi ions. Ye , o my bes
knowledge, none o he sys ems o e o e ic logic deals wi h Wh-ques ions
and p esupposi ions o ques ions in a plausible way. This is unsa is ac o y,
as Wh-ques ions a e e en mo e equen han Yes-No ques ions in ou e e-
yday e nacula .4
To ob ain a li e al analysis o na u al language sen ences, I am going o
apply Tichý’s (1988) T anspa en In ensional Logic (TIL) wi h i s p oce-
du al seman ics, namely, i s e sion as in oduced in (Duží, Jespe sen and
Ma e na 2010). The analysis o empi ical Wh-ques ions ans o ms in he
TIL o malism in o λ- e ms deno ing p ocedu es ha p oduce α-in ensions
( unc ions wi h he domain o possible wo lds ω and imes τ, and alues o
ype α) whe e α is no a u h- alue. The sough answe should p o ide an
objec o ype α, which is he alue o he α-in ension asked o in he ac ual
wo ld a he ime o e alua ion. Since o dina y e o e ic logics do no usually
deal wi h Wh-ques ions, (Duží and Fai 2021) adjus ed Gen zen’s sys em
o na u al deduc ion o TIL so ha he sys em can answe no only Yes-
No ques ions by keywo d sea ching bu also answe Wh-ques ions by in e -
ing compu able knowledge om na u al-language ex s.5 The pape
3 See, o ins ance, Ha ah (2002) o Peliš and Maje (2011). Fo a sys em based
on ele an logic ha can p o ide axioms and ules o dealing wi h Yes-No ques-
ions, see, o ins ance (Punčochář 2020).
4 The e a e a ew sys ems dealing wi h Wh-ques ions, see, o ins ance,
G oenendijk (2003), Haida (2008), Hamblin (1973), Essbe ge (online) o Ka unen
(1977). Ye , none o hem co e s his issue in a sa is ac o y way. Thei summa y
and app aisal om he poin o iew o applica ion in TIL can be ound in Číhalo á,
Duží (2022).
5 Compu able o in e able knowledge has been in oduced as a golden middle way
be ween wo ex emes, namely explici and implici knowledge. Classical epis emic
sys ems deal wi h explici and implici knowledge. The o me p e en s he pa adox
o logical/ma hema ical omniscience by dep i ing he agen s o any in e en ial abil-
i ies, as hey know only hose pieces o knowledge ha a e explici ly eco ded in
hei knowledge base. On he o he hand, dealing wi h implici knowledge
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 69
O ganon F 30 (1) 2023: 66–101
desc ibes a use ul logical echnique o de i ing answe s o Wh-ques ions
based on a gi en knowledge base ha can be bo h an agen ’s base o e en
na u al language ex s. I consis s o en iching he sys em o na u al deduc-
ion wi h special ules oo ed in he ich seman ics o a na u al language.
In addi ion, special echnical ules a e speci ied o ope a e in o hype in en-
sional con ex s; see Duží, Jespe sen (2015) and Jespe sen, Duží (2022).
In (Číhalo á, Duží 2022) he analysis o agen s’ ac i i ies is b ie ly ou -
lined. The goal o his pape is o p opose a de ailed analysis o agen s’
dynamic ac i i ies bo h om he poin o iew o hei speci ica ions and
answe ing ques ions on such ac i i ies. The analysis akes accoun o ime,
i.e. sen ences in he pas , p esen o u u e enses wi h e e ence o he ime
when his o ha happened, is happening o will happen.
The es o he pape is o ganised as ollows. Sec ion 2 summa ises he
basic p inciples o T anspa en In ensional Logic (TIL). In Sec ion 3, I
b ie ly ep oduce he concep ual-o ien ed classi ica ion o Wh-ques ions as
o (Číhalo á, Duží 2022). The main no el y o his pape is p esen ed in
Sec ion 4; i is he analysis o agen s’ dynamic ac i i ies speci ied in pas ,
p esen o u u e enses oge he wi h he agen s’ lea ning new concep s by
ques ioning and answe ing. Concluding ema ks and p oposals o u he
esea ch can be ound in Sec ion 5.
2.
Basic P inciples o TIL
Pa el Tichý, he T anspa en In ensional Logic (TIL) ounde , was in-
spi ed by F ege’s seman ic iangle. F ege cha ac e ised he sense o an
p esupposes ha he agen s would be able o de i e all he logical consequences o
hei explici ly eco ded pieces o knowledge, i only hey had an in ini e amoun o
ime and esou ces a hei disposal. Hence, implici knowledge ine i ably yields he
pa adox o logical/ma hema ical omniscience. Since bo h no ions a e no ealis ic in
case o modelling beha iou o in elligen bu esou ce bounded agen s, we in oduce
he no ion o in e able knowledge. The idea is simple. Ha ing an agen wi h some
in e en ial abili ies and an explici knowledge base, we compu e maximal limi o
knowledge hey a e able o in e by applying he ules o in e ence he agen mas e s.
Fo de ails, see Duží, Menšík (2017).
70 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
exp ession as he ‘mode o p esen a ion’. Tichý de ines his mode o p esen-
a ion as an abs ac , algo i hmically s uc u ed p ocedu e ha p oduces
he objec deno ed by he exp ession o , in igo ously de ined cases, ails o
p oduce a deno a ion i he e is none.6 This is because he e a e non-deno -
ing e ms ha ha e a pe ec meaning, like ‘ he g ea es p ime numbe ’ o
‘ he alue o he co angen unc ion a he numbe π’. Ma hema icians had
ob iously o unde s and he sense o hese e ms i s , and only hen could
hey p o e ha he e a e no such numbe s. Hence, in TIL, he meaning o
an exp ession is unde s ood as a con ex -in a ian p ocedu e encoded by a
gi en exp ession. By ‘con ex in a ian ’, we mean his. The p ocedu e en-
coded by an unambiguous exp ession is one and he same (up o p ocedu al
isomo phism) independen ly o he con ex in which he exp ession is used.7
I he exp ession is ambiguous, i is u nished wi h mo e han one p ocedu e
co esponding o i s di e en meanings.
Tichý de ined six kinds o meaning p ocedu es and called hem cons uc-
ions. The e a e wo kinds o a omic cons uc ions ha supply inpu objec s
o be ope a ed on by molecula cons uc ions. They a e T i ializa ion and
Va iable. A T i ialisa ion p esen s an objec X wi hou he media ion o
any o he p ocedu es. Using he e minology o p og amming languages, he
T i ialisa ion o X, deno ed by ‘0X’, is jus a poin e o e e ence o X.
T i ializa ion can p esen an objec o any ype, e en ano he cons uc ion
C. Hence, i C is a cons uc ion, 0C is said o p esen he cons uc ion C,
whe eby C occu s hype in ensionally, i.e. in he non-execu ed mode. Va ia-
bles p oduce objec s dependen ly on alua ions; hey a e said o -cons uc .
The execu ion o a T i ialisa ion o a a iable ne e ails o p oduce an
objec . Howe e , since TIL is a logic o pa ial unc ions, he execu ion o
some o he molecula cons uc ions can ail o p esen an objec o he ype
6 See Tichý (1988). A simila philosophy o meaning as a ‘gene alized algo i hm’
can be ound in (Moscho akis 2006); his concep ion has been u he de eloped by
Loukano a (2009). TIL p ocedu al iewpoin is also no a om he idea o algo-
i hmic logic, see Li, B. (2022). 4936. h ps://doi.o g/10.20935/AL4936.
7 Fo he de ini ion o p ocedu al isomo phism, see (Duží 2019). B ie ly, he e is
no unique c i e ion o p ocedu al isomo phism and any language, any discou se. In
p ac ice, p ocedu es a e isomo phic i hei speci ica ion is iden ical up o α-equi a-
lence o es ic ed β-equi alence.

Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 71
O ganon F 30 (1) 2023: 66–101
hey a e yped o p oduce. When his happens, we say ha a gi en con-
s uc ion is -imp ope .
The e a e wo kinds o molecula cons uc ions, which co espond o
λ
-
abs ac ion and applica ion in he λ-calculi, namely Closu e and Composi-
ion. λ-Closu e, [λx1…xn X], is he e y p ocedu e o p oducing a unc ion
wi h he alues -p oduced by he p ocedu e X, by abs ac ing o e he
alues o he a iables x1, …, xn o p o ide unc ional a gumen s. No Closu e
is -imp ope o any alua ion , as a Closu e always -cons uc s a unc-
ion (which may be, in an ex eme case, a degene a e unc ion unde ined a
all i s a gumen s). Composi ion, [X X1…Xn], is he e y p ocedu e o apply-
ing a unc ion p oduced by X (i any) o he uple a gumen 〈a1, …, an〉 (i
any) p oduced by he p ocedu es X1, …, Xn. A Composi ion is -imp ope
as soon as is a pa ial unc ion no de ined a i s uple a gumen o i one
o mo e o i s cons i uen s X, X1, …, Xn a e -imp ope .8
TIL being a hype in ensional sys em, each cons uc ion C can occu no
only in execu ion mode so as o p oduce an objec (i any) when being
execu ed bu also as an objec in i s own igh on which o he (highe -o de )
cons uc ions ope a e. The T i ialisa ion o C causes C o occu jus p e-
sen ed as an a gumen , as men ioned abo e. Ye some imes, we need o
cancel he e ec o T i ialisa ion and ade he mode o C o execu ion
mode. Double Execu ion, 2C, does jus ha ; i execu es C wice o e . I C
-cons uc s a cons uc ion D ha in u n -cons uc s an en i y E, hen
2C -cons uc s E. O he wise, 2C is -imp ope . Hence, o any cons uc ion
C, his law is alid: 20C=C.
DEFINITION 1 (cons uc ion)
(i) Va iables x, y, … a e cons uc ions ha cons uc objec s (i.e., ele-
men s o hei espec i e anges) dependen ly on a alua ion unc ion
; hey -cons uc .
8 In he es o his sec ion, I d aw on he s anda d exposi ion o he undamen als
o TIL, as p esen ed in o he pape s ( o ins ance in Jespe sen, Duží (2022) o Duží,
Fai (2021)), wi h jus a ew mino adjus men s. T ue, since TIL has become a well-
known sys em, his exposi ion could ha e been mo e condensed; ye , in he e o o
making e e y hing comp ehensi e and con enien o a eade , I lea e his pa in
ull de ails.
72 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
(ii) Whe e X is an objec wha soe e (e en a cons uc ion), 0X is he
cons uc ion T i ialisa ion ha cons uc s X wi hou any change.
(iii) Le X, Y1, …, Yn be a bi a y cons uc ions. Then he Composi ion
[X Y1…Yn] is he ollowing cons uc ion. Fo any , he Composi ion
[X Y1…Yn] is -imp ope i one o mo e o X, Y1, …, Yn a e -imp ope ,
o i X does no -cons uc a unc ion ha is de ined a he n- uple
o objec s -cons uc ed by Y1, …, Yn. I X does -cons uc a -p ope
unc ion, hen [X Y1…Yn] -cons uc s he alue o his unc ion a
he n- uple.
(i ) (λ-) Closu e [λx1…xm Y] is he ollowing cons uc ion. Le x1, x2, …, xm
be pai -wise dis inc a iables and Y a cons uc ion. Then [λx1…xm Y]
-cons uc s he unc ion ha akes any membe s B1, …, Bm o he
espec i e anges o he a iables x1, …, xm in o he objec (i any) ha
is (B1/x1,…,Bm/xm)-cons uc ed by Y, whe e (B1/x1,…,Bm/xm) is like
excep o assigning B1 o x1, …, Bm o xm.
( ) Whe e X is an objec wha soe e , 1X is he cons uc ion Single Exe-
cu ion ha -cons uc s wha X -cons uc s. Thus, i X is a -im-
p ope cons uc ion o no a cons uc ion as all, 1X is -imp ope .
( i) Whe e X is an objec wha soe e , 2X is he cons uc ion Double Ex-
ecu ion. I X is no i sel a cons uc ion, o i X does no -cons uc
a cons uc ion, o i X -cons uc s a -imp ope cons uc ion, hen
2X is -imp ope . O he wise 2X -cons uc s wha is -cons uc ed by
he cons uc ion -cons uc ed by X.
( ii) No hing is a cons uc ion, unless i so ollows om (i) h ough ( i).
Wi h cons uc ions o cons uc ions, cons uc ions o unc ions, unc ions,
and unc ional alues in TIL s a i ied on ology, we need o keep ack o
he a ic be ween mul iple logical s a a. The ami ied ype hie a chy dis-
cha ges ha ask. The ype o i s -o de objec s includes all objec s ha
a e no cons uc ions. The e o e, i includes no only he s anda d objec s
o indi iduals and u h alues bu also se s, unc ional mappings and unc-
ions de ined on possible wo lds (i.e., he in ensions ge mane o possible-
wo ld seman ics, PWS in ensions). The ype o second-o de objec s in-
cludes cons uc ions o i s -o de objec s and unc ions wi h such
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 73
O ganon F 30 (1) 2023: 66–101
cons uc ions in hei domain o ange. The ype o hi d-o de objec s in-
cludes cons uc ions o i s - o second-o de objec s and unc ions wi h such
cons uc ions in hei domain o ange; and so on ad in ini um.
DEFINITION 2 ( ami ied hie a chy o ypes). Le B be a base, whe e a base
is a collec ion o pai -wise disjoin , non-emp y se s. Then:
T1 ( ypes o o de 1).
i) E e y membe o B is an elemen a y ype o o de 1 o e B.
ii) Le α, β1, ..., βm (m > 0) be ypes o o de 1 o e B. Then he collec ion
(α β1 ... βm) o all m-a y pa ial mappings om β1 × ... × βm in o α is a
unc ional ype o o de 1 o e B.
iii) No hing is a ype o o de 1 o e B unless i so ollows om (i) and (ii).
Cn (cons uc ions o o de n)
i) Le x be a a iable anging o e a ype o o de n. Then x is a cons uc-
ion o o de n o e B.
ii) Le X be a membe o a ype o o de n. Then 0X, 1X, 2X a e cons uc-
ions o o de n o e B.
iii) Le X, X1, ..., Xm (m > 0) be cons uc ions o o de n o e B. Then
[X X1... Xm] is a cons uc ion o o de n o e B.
i ) Le x1, ..., xm, X (m > 0) be cons uc ions o o de n o e B. Then
[λx1...xm X] is a cons uc ion o o de n o e B.
) No hing is a cons uc ion o o de n o e B unless i so ollows om Cn
(i)-(i ).
Tn+1 ( ypes o o de n + 1)
Le *n be he collec ion o all cons uc ions o o de n o e B. Then
i) *n and e e y ype o o de n a e ypes o o de n + 1.
ii) I m > 0 and α, β1, ..., βm a e ypes o o de n + 1 o e B, hen (α,
β1, ..., βm) (see T1 ii)) is a ype o o de n + 1 o e B.
74 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
iii) No hing is a ype o o de n + 1 o e B unless i so ollows om (i)
and (ii).
Fo he pu poses o na u al-language analysis, we a e usually assuming he
ollowing base o g ound ypes:
ο: he se o u h- alues {T, F};
ι: he se o indi iduals ( he uni e se o discou se);
τ: he se o eal numbe s (doubling as imes);
ω: he se o logically possible wo lds ( he logical space).
We assume ha he uni e se o discou se ι is mul i- alued and consis s o
a leas wo elemen s, hough he e I lea e aside he ca dinali y o his basic
ype.
Empi ical exp essions deno e empi ical condi ions, which may o may
no be sa is ied a he wo ld/ ime pai selec ed as poin s o e alua ion.
These empi ical condi ions a e modelled as (PWS-)in ensions. In ensions
a e en i ies o ype (βω): mappings om possible wo lds o an a bi a y
ype β. The ype β is equen ly he ype o he ch onology o α-objec s,
i.e., a mapping o ype (ατ). Thus α-in ensions a e mos ly unc ions o ype
((ατ)ω), abb e ia ed as ‘ατω’.9 Ex ensional en i ies a e en i ies o a ype α
whe e α ≠ (βω) o any ype β. Whe e he a iable w anges o e β and
o e τ, he ollowing ou line o a Closu e essen ially cha ac e ises he logical
syn ax o empi ical language: λwλ […w…. …].
Examples o equen ly used α-in ensions a e: p oposi ions o ype οτω,
p ope ies o indi iduals o ype (οι)τω, bina y ela ions-in-in ension be ween
indi iduals o ype (οιι)τω, o ices o ype ιτω and hype in ensional a i udes
o ype(οι∗n)τω. Logical objec s like u h unc ions and quan i ie s a e ex-
ensional: ∧, ∨, ⊃ a e o ype (οοο), and ¬ o ype (οο).
9 We de ine (PWS-)in ensions as unc ions wi h he domain o possible wo lds.
T ue, mos equen ly, ime plays he ole o he second modal pa ame e , hough
no always. Fo ins ance, assuming ha physical laws o na u e a e nomically bu
no analy ically necessa y, as physics is an empi ical science, we model hese in en-
sions by cons uc ion o his o m: λw ∀ […] → οω.
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 81
O ganon F 30 (1) 2023: 66–101
No e ha he ques ion ans o ms in o a cons uc ion o an indi idual
o ice, as i should be. The agen would like o know he alue o his o ice.
Ano he equen ype o in ensions is he p ope y o indi iduals, an
objec o ype (οι)τω. Fo ins ance, he di ec answe o he ques ion “Which
a e he p i a e hospi als loca ed in Lowes o ?” should con ey a se (o ype
(οι)) o indi iduals. The e a e wo kinds o possible di ec answe s. An
exhaus i e answe con eys a comple e lis o indi iduals wi h he p ope y
o being a p i a e hospi al in Lowes o , while an incomple e answe p o-
ides jus some o hem. Anyway, in bo h cases, he answe should be con-
clusi e; i means ha he indi iduals belonging o his lis should be e e ed
o di ec ly. An indi ec desc ip ion o an indi idual would no be sa is ac-
o y.16 Fo ins ance, he answe “They a e he p i a e hospi als loca ed in
he mos eas e n ci y o England” is no conclusi e. The agen would ha e
o go on asking, “Which is he mos eas e n ci y o England?” and “Which
a e he p i a e hospi als in he mos eas e n ci y o England?” and so on.
Thus, he exhaus i e answe o he ques ion would be, o ins ance, he
se : {Ca l on Cou , Ai ey Close, Beccles Hospi al Inpa ien s, Eas Poin
Consul ing Rooms, Andaman Su ge y, James Page Hospi al, Eas Coas
Communi y, The Ve e ina y Su ge y, C es View Medical Cen e}.
The analysis o he ques ion ha cons uc s a p ope y o indi iduals
( ha a e asked o ) is his.
λwλ [λx [[[0P i a e 0Hospi al]w x] ∧ [0Loca ed-inw x 0Lowes o ]]] → (οι)τω
Types. x → ι: he a iable anging o e indi iduals; P i a e/((οι)τω(οι)τω):
p ope y modi ie : an analy ic unc ion ha assigns o a p ope y ano he
(modi ied) p ope y;17 Hospi al/(οι)τω; Loca ed-in/(οιι)τω; Lowes o /ι.
One can also ask o he alue o an a ibu e a an a gumen like he
sala y o somebody. The possible answe o he ques ion “Wha is John’s
sala y?” is a numbe , and he ques ion deno es a magni ude o ype ττω.
16 This p oblem has been deal wi h in Duží (2022).
17 The analyses o p ope y modi ie s has been in oduced in Jespe sen, Ca a a,
Duží (2017) o in Duží (2017).

82 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
3.1 Classi ica ion o Wh-ques ions
Číhalo á & Duží (2022) in oduce he classi ica ion o Wh-ques ions
based on he ype o a possible answe . They show ha o ou pu pose,
he linguis ic classi ica ions a e oo coa se-g ained and non-plausibly o i-
en ed. Fo he needs o a mul i-agen sys em, we classi y ques ions no only
om he linguis ic poin o iew bu also om he logical poin o iew,
wi h espec o a domain o in e es and he s uc u e o he agen ’s
knowledge base. The au ho s dis inguish be ween s a ic en i ies, like neces-
sa y ela ions be ween p ope ies o indi iduals and dynamic en i ies, like
ac i i ies which o m p ocesses. Ac i e ac ions and passi e e en s a e ac-
i i ies. Each ac i i y can in ol e o he objec s ha a e called hei pa ic-
ipan s.
The speci ica ion o ac i i ies is based on he linguis ic heo y o e b
alency ames.18 F om he logical poin o iew, we deal wi h he e b
ph ases as deno ing a unc ion ha is applied o i s a gumen s. The numbe
o a gumen s is con olled by he con en e b alency. The e a e se e al
ypes o alency. An impe sonal (a alen ) e b has no subjec o a dummy
subjec . “I ains.” is a ypical example. He e he g amma ic subjec ‘i ’ is
jus a dummy subjec because i does no e e o any conc e e objec .19 An
in ansi i e (mono alen ) e b has jus one a gumen , he subjec S; “John
18 Fo he linguis ic heo y o e b alency ames, see Ho ák (1998) o Rambousek,
Hla áčko á (2011). Číhalo á (2016) p oposed on ology o e en s based on he heo y
o e b alency ames. This heo y is no unlike Chomsky’s θ- heo y, which is con-
ce ned wi h he dis ibu ion and assignmen o hema ic oles o a gumen s. The
he a c i e ion desc ibes he speci ic ma ch be ween a gumen s and hema ic oles
in he logical o m o a sen ence. (I am g a e ul o he anonymous e iewe o
d awing my a en ion o his heo y.) Ye , since ou esea ch is a pa o a b oade
p ojec on linguis ic and logical na u al language analysis and p ocessing, and since
in his p ojec we coope a e wi h he cen e o compu a ional linguis ics in Masa yk
Uni e si y o B no, we o e o he heo y o e b alency ames. This heo y is
suppo ed by he cen e, whe e he lexicon o e b alencies (Ve baLex) has been
de eloped.
19 Lo s o languages, including Romance and Sla onic ones, d op he dummy sub-
jec (‘i ’, ‘es’, …) al oge he , and make sen ences jus wi h a e b in hi d pe son
singula .
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 83
O ganon F 30 (1) 2023: 66–101
(S) is singing.” A ansi i e (di alen ) e b has wo a gumen s, an agen
(A) and a pa ien (P), as in “John (A) kicked he ball (P).” A di ansi i e
e b has h ee a gumen s, an agen and wo pa ien s, o ins ance, in “John
(A) passed he ball (P) o Tom (P).” The e a e also a ew e bs wi h mo e
han h ee a gumen s (poly alen , like i ansi i e); ye hey mos ly a ise
by alency inc easing, whe e causa i es o applica i es a e ypical alency
inc easing de ices.20
Ve b alency ames de e mine he obliga o y and acul a i e a gu-
men s, i.e. hema ic oles o a gi en e b, oge he wi h hei ypes. Facul-
a i e a gumen s can be missing, o cou se. Fo ins ance, he e b ‘buy’ can
occu in se e al sen ences wi h a di e en numbe o a gumen s like “Tom
bough a book”, “Tom bough a book in Pa is”, “On F iday, Tom bough
a book”, “Tom bough a book o Jane in Pa is”, e c. In ou analysis, we
ha e o ake hese a ie ies in o accoun . Linguis s ha e c ea ed many clas-
si ica ions based on e b alency ames, o ins ance, VALLEX o Ve -
baLex.21
John Sowa (2000) p oposed a speci ica ion ool o knowledge ep esen-
a ion, whe e he adop ed a linguis ic app oach o e bs. He de eloped he
sys em o concep ual g aphs in which Pei ce’s logic is combined wi h he
seman ic ne wo ks known om a i icial in elligence. Fo he alency pa -
icipan s, Sowa uses he e m ‘ hema ic oles’ o ‘case ela ions.’ His sum-
ma y o all he hema ic oles can be ound in (Sowa 2000, pp. 506-510) o
in he web sou ce Thema ic oles. Sowa dis inguishes se e al ypes o he-
ma ic oles, o ins ance, Agen , Bene icia y, Des ina ion, Du a ion, E ec-
o , Expe ience , Ins umen , Loca ion, Ma e , Pa ien and so on.22 The-
ma ic ole o he ype o a pa icipan exp esses he ole ha a noun ph ase
plays o he ac i i y desc ibed by a go e ning e b. F om he iewpoin o
logic, i is he ela ion be ween wo en i ies whe e one is an ac i i y (ex-
p essed by he e b), and he o he is an a ibu e (exp essed mos ly by a
noun, ad e b, numbe o adjec i e).
The numbe and he ca ego ies o pa icipan s depend on he espec i e
domain o in e es and he unc ions o he sys em o agen s. In his pape ,
20 Fo de ails, see Dixon (2000).
21 See, o ins ance Lopa ko á e al. (2006) and Hla áčko á, Ho ák (2006).
22 Fo de ails, see Sowa (2000, 508-510).
84 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
I will use he ollowing equen kinds o a ibu es ha can be assigned o
an ac i i y:
Pa – objec a ec ed by he ac i i y
Ben – bene icien (somebody who has bene i ed om he ac i i y)
Man – he manne o he ac i i y execu ion (measu e, speed e c.)
Ins – ins umen
Time – when
Loc – he place o ac i i y
Di 1 – he di ec ion o ac i i y – om whe e
Di 2 – he di ec ion o ac i i y – which way
Di 3 – he di ec ion o ac i i y – whe e o
Wh-ques ions conce n he pa icipan s o ac i i ies; we ask o hei alues
in a wo ld and ime o e alua ion. Hence, we can dis inguish ques ions abou
he p ocess i sel (wha is going on?) om Wh-ques ions on he p ima y
agen and o he pa icipan s o a gi en ac i i y. Fo ins ance, assume we
ha e he sen ence “John ( he agen ) is going ( he ac i i y) o London (Di 3)
by ca (Ins ) in an a e age speed o 50 miles pe hou (Man).” Then we can
ask, “Wha is John doing?”, “Who is going o London?”, “How quickly does
John go o London?” e c.
3.2 Hype in ensional ques ions abou concep s
A pa icula ca ego y o ques ions conce ns hype in ensional ques ions
abou a gi en concep . The agen s should be able o lea n om expe ience
h ough mu ual communica ion wi h hei ellow agen s. In such a commu-
nica ion, i may happen ha a ecei ing agen b does no ‘know’ a concep
ha is a cons i uen o a sende ’s message. By ‘knowing a concep ’ C, we
mean ha ing he concep C in one’s on ology. In such a si ua ion, he e-
cei ing agen b can ask o an explica ion o a de ini ion o he unknown
concep . When asking o he explica ion o concep C he agen does no
alk abou he objec p oduced by C. Ra he , he concep , i.e. he closed
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 85
O ganon F 30 (1) 2023: 66–101
cons uc ion C i sel , is a subjec ma e ha is asked o . Such a con ex
whe e he cons uc ion C is jus p esen ed as an a gumen a he han ex-
ecu ed o p oduce an objec is hype in ensional. In (Duží & Voj áš 2008), a
special kind o ques ion is in oduced, namely a ques ion wi h he pe o ma-
i e Un ecognized, he a gumen o which is an unknown concep C. The
answe is hen o ype Re ine, whe e he message p o ides a concep C’,
which e ines he unknown concep C.
Re inemen has been igo ously de ined abo e (De .5). B ie ly, by e in-
ing an a omic concep o an objec O, we mean disco e ing a molecula
concep ha p oduces he same objec O. In ma hema ics, e ining usually
conce ns de ini ions like “a g oup is a se G equipped wi h a bina y ope a-
ion ha combines any wo elemen s o G o o m ano he elemen o G in
such a way ha g oup axioms a e sa is ied, namely associa i i y, he exis -
ence o he neu al elemen in G and in e ibili y.” He e he a omic concep
o be e ined is ha o a ‘g oup’. The molecula concep e ining ‘g oup’ is
encoded by he de iniens, namely ‘a se G equipped wi h a bina y ope a ion
ha combines any wo elemen s o G o o m ano he elemen o G in such
a way ha g oup axioms a e sa is ied, namely associa i i y, he exis ence
o he neu al elemen in G and in e ibili y’. In he case o empi ical con-
cep s, i is mo e plausible o speak abou explica ion. The eason is his. To
say ha a molecula concep C is a e inemen o an a omic empi ical con-
cep D is isky. I would be a e inemen only i he molecula concep C
we e analy ically equi alen o he o iginal concep D, which means ha
bo h a e he concep s o he same objec O/ατω. Howe e , in he mos in-
e es ing cases o empi ical concep s o PWS-in ensions we use a Ca napian
explica ion a he han a de ini ion p ope . Then equi alence is undoub edly
no gua an eed, o one can ha dly check he iden i y o he in ensions p o-
duced by he wo concep s. Ra he , a new molecula concep C (explica um)
should de ine an in ensional objec O ha is as close as possible o he
objec e e ed o by an inexac (p escien i ic) concep D (explicandum).
In Meaning and Necessi y (1947), Ca nap cha ac e ises explica ion as
ollows:
The ask o making mo e exac a ague o no qui e exac concep
used in e e yday li e o in an ea lie s age o scien i ic o logical
de elopmen , o a he o eplacing i by a newly cons uc ed,
86 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
mo e exac concep , belongs among he mos impo an asks o
logical analysis and logical cons uc ion. We call his he ask o
explica ing, o o gi ing an explica ion o , he ea lie concep […]
(Ca nap 1947, pp. 7-8)
Keeping his di e ence in mind, I use he e m ‘ e inemen ’ o bo h cases,
including he explica ion o empi ical concep s. In mos cases o explica ing
he concep unknown o an agen , his simpli ica ion is ha mless.
4. Agen s’ dynamic ac i i ies
The basic idea o he analysis is due o (Tichý 1980). I s adjus men and
simpli ica ion a e in oduced in (Duží 2010). Tichý d aws a dis inc ion be-
ween episodic and a ibu i e e bs. A ibu i e e bs asc ibe p ope ies o
indi iduals, and hei s uc u e is usually a copula ollowed by an adjec i e
o noun; o ins ance, ‘is happy’, ‘is ed’, ‘looks speedy’, ‘is a s uden ’ a e
a ibu i e e bs. On he o he hand, episodic e bs exp ess ac ions pe -
o med by objec s. Fo ins ance, i John is ge ing up, i would be insu i-
cien o analyse his ac i i y by assigning he p ope y o ge ing up o
John. Ra he , John is doing he ac i i y o ge ing up. Fo example, he
sen ence “John is d i ing om B ussels o Pa is a he a e age speed o 90
km/h” should be analysed as desc ibing a ime-consuming p ocess consis ing
o a se ies o ac ions and e en s. In (Číhalo á, Š ěpán 2014), he basic idea
o speci ying e en on ology by means o e b alency ames was in o-
duced, and (Číhalo á, 2016) p oposed i s u he adjus men . I consis s, in
pa icula , in e ining he ype o ac ion execu ed wi hin a gi en p ocess.
Fo ins ance, he speci ica ion o he p ocess Cha les is d i ing om P ague
o München by ain a he speed o 90 km/h is de e mined by he sense o
he e b ‘ o d i e’ oge he wi h i s a gumen s (who is d i ing – he ac o ,
when is (s)he d i ing, om whe e, o whe e, by wha kind o a ehicle, in
which speed, e c.).
4.1 Agen s’ ac i i ies in he p esen
F om he logical poin o iew, an episodic e b deno es a ela ion-in-
in ension Do be ween an indi idual o ype ι ( he ac o ) and an ac i i y.

Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 87
O ganon F 30 (1) 2023: 66–101
Using a gene al placeholde α o he ype o ac i i y, Do hus ob ains he
ype (οια)τω.23
As men ioned abo e, each ac i i y has se e al pa icipan s (i.e. assign-
men s o an a ibu e o he ac i i y), and he alency o he e b de e -
mines he compulso y pa icipan s and he maximal numbe o acul a i e
pa icipan s. The a ibu es can be o a ious kinds like indi iduals, p op-
e ies, quan i ies, e c. Typical kinds o a ibu es ha e been speci ied abo e.
They a e Pa (objec a ec ed by he ac i i y), Ben (who has a bene i om
he ac i i y), Manne (manne o he ac i i y execu ion), Ins (ins umen ),
Time (when), Time1 ( ime when he ac i i y s a ed), Time2 ( ime when
he ac i i y ended), Loc (loca ion o he ac i i y), Di 1 (di ec ion o e en
– om whe e), Di 2 (di ec ion o e en – whe e h ough), Di 3 (di ec ion
o e en – whe e o). I needed, o he kinds o a ibu es can be speci ied.
Fo he pu pose o he sys em implemen a ion, we only mus keep he se-
lec ed keywo ds ixed.
The ype o assigning an a ibu e o an ac i i y is he ela ion in in en-
sion be ween an objec o ype β and he ac i i y ( ype α); whe e β can be
a p ope y o indi iduals like being a ain, o a numbe o ype τ ( ime),
indi idual ι (like John, P ague, B ussels) e c., acco ding o he kind o an
a ibu e. Thus, we ha e a gene al ype o pa icipan Pa /(οβα)τω. I mus
be a ela ion-in-in ension, as one and he same ac i i y can be pe o med
wi h di e en ins umen s a di e en imes, and so like. Fo ins ance, John
can go om P ague o B ussels by ain, and nex ime he can o e o a
plane.
23 In his pape , I o en elease yping and use ins ead placeholde s like α, β, δ o
en i ies oo complica ed om he yping poin o iew. As we all know well, yped
languages and calculi a e use ul and easy o wo k wi h because yping p e en s a
use om making silly mis akes when speci ying p ocedu es. Ye , oo s ong yping
can some imes be es ic i e. Fo his eason, yped unc ional p og amming lan-
guages a e usually polymo phic, o ype con ol is no oo s ic ; in case o a yping
e o , he in e p e e only in o ms he p og amme and lea es he decision o hem.
As TIL is a yped lambda calculus, in i s compu a ional a ian TIL-Sc ip , we also
aim o implemen such use ul ea u es. P oposals o he polymo phic TIL sys em
ha e been in oduced in Duzi (1993), Pezla (2020) and Pezla (2022). Fo a bene -
olen ype checking algo i hm, see, e.g., Duží,Ma ie & Fai ,Ma ie (2019).
88 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
A gene al pa e n o he analysis o an ac i i y P → α wi h he ac o
A → ι and pa icipan s Pa -i/(οβα)τω ha assign a ibu es Xi → βi o P
is his:24
λwλ [[0Dow A P] ∧ [0Pa -1w X1 P] ∧
[0Pa -2w X2 P] ∧…∧ [0Pa -nw Xn P]]
Fo ins ance, he analysis o he sen ence “John goes o B ussels by ain”
comes down o his cons uc ion.
λwλ [[0Dow 0John 0Go]∧ [0Ins w 0T ain 0Go] ∧
[0Di 3w 0B ussels 0Go]]
I may happen ha a ano he ime John will go o B ussels by plane. Then
we ha e
λwλ [[0Dow 0John 0Go] ∧
[0Ins w 0Plane 0Go] ∧ [0Di 3w 0B ussels 0Go]]
Wh-ques ions abou John’s ac i i y would be, o ins ance: Wha does John
do? Whe e does John go? The con en o hese ques ions ans o ms in o
cons uc ions like ( a iables wha → α, whe e → ι)
λ
w
λ
λ
wha [0Dow 0John wha ]
λ
w
λ
λ
whe e [[0Dow 0John 0Go] ∧ [0Di 3w whe e 0Go]]
The echnique o deducing answe s o such Wh-ques ions has been in-
oduced in Duží, Fai (2020) and (2021). I is an adjus ed sys em o na u al
deduc ion wi h special ules oo ed in he ich seman ics o na u al language
and some echnical TIL ules s emming om he need o wo k wi hin a
hype in ensional con ex . Classical na u al deduc ion ules can be applied
only o cons i uen s o a cons uc ion. Fo his eason, we need hese special
24 The i s p oposal o such an analysis o ac i i ies wi h pa icipan s has been
in oduced in Duží (2021). In his pa ag aph, I in oduce a sligh ly adjus ed and
co ec ed analysis. In pa icula , I do no apply he ela ion-in-in ension Assign (an
a ibu e o an ac i i y), as his en i y is supe luous and we can ob ain a mo e
elegan solu ion wi hou i .
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 89
O ganon F 30 (1) 2023: 66–101
echnical ules.25 In p inciple, answe s o such Wh-ques ions a e de i ed by
uni ying ma ching e ms by means o subs i u ing he alues o a iables
like wha , whe e, and so like. In ou simple example, he answe s would be
wha = 0Go, whe e = 0B ussels.
I agen b has in his on ology he speci ica ion o all he possible pa ic-
ipan s o an ac i i y, and i b ob ains an incomple e message whe e some
pa icipan s a e missing, hen b can ask his ellow agen s o comple e he
missing pieces o knowledge. Fo ins ance, when ecei ing he i s message
abou John’s going o B ussels by ain, he agen can send ano he que y
message asking om whe e does John go o B ussels. To his end, we apply
he me hod o analysis o Wh-ques ions, as in oduced abo e. The con en
o he que y is hen his.
λwλ λd [[0Dow 0John 0Go] ∧
[0Ins w 0T ain 0Go] ∧ [0Di 1w d 0Go] ∧ [0Di 3w 0B ussels 0Go]]
A possible answe o his Wh-ques ion is he message wi h his con en .
λwλ [[0Dow 0John 0Go] ∧[0Ins w 0T ain 0Go] ∧
[0Di 1w 0P ague 0Go] ∧ [0Di 3w 0B ussels 0Go]]
The answe is ob ained by subs i u ing P ague o he a iable d using he
agen s’ knowledge base.26 In case he e a e wo o mo e ac o s o he ac i -
i y, we can apply he ela ion-in-in ension Do’/(ο(οι)α)τω. Fo ins ance, he
sen ence “John and Tom go o B ussels by plane on Ap il 1s ” is u nished
wi h his analysis.
λwλ [[0Do’w λx [[x= 0John] ∨ [x= 0Tom]] 0Go] ∧
[0Ins w 0Plane 0Go] ∧ [0Di 3w 0B ussels 0Go] ∧
[0Timew 0Ap il1 0Go]]
The abo e sen ence is unde speci ied, as i is no clea whe he John and
Tom a e going on hei own o oge he . Ye , he analysis is unambiguous,
25 See, o ins ance, Duží,Ma ie, Jespe sen, B. (2015) and Jespe sen, B., Duží,Ma ie
(2022), whe e he ules o exis en ial quan i ica ion in o hype in ensional con ex s
ha e been in oduced.
26 Fo de ails on deducing answe s o Wh-ques ions by applying he sys em o
na u al deduc ion adjus ed o TIL, see Duží, Fai (2021).
90 Ma ie Duží
O ganon F 30 (1) 2023: 66–101
as John and Tom a e he wo ac o s o he same ac i i y. Hence, hey a e
going oge he . I hey wen each on hei own, i would be wo di e en
ac i i ies wi h di e en ac o s, e en i he o he pa icipan s we e iden i-
cal.27
4.2 Agen s’ ac i i ies in pas o u u e
Ano he ad an age o his app oach is his. Since in TIL, we ha e wo
modal pa ame e s, ime and possible wo lds, we can easily speci y ac i i ies
execu ed in pas o u u e and model he dynamic beha iou and easoning
o agen s. I an ac i i y was execu ed in he pas o will be execu ed in
u u e, he sen ence should con ain a e e ence o he ime when his o ha
happened o will happen. Fo ins ance, he sen ence “John will go o B us-
sels by plane” ecei es his analysis.
λwλ ∃ ' [[0Dow ’ 0John 0Go] ∧ [ ’ > ] ∧
[0Ins w 0Plane 0Go] ∧ [0Di 3w 0B ussels 0Go]]
No e ha he a ibu es Ins and Di 3 a e ex ensionalised wi h espec o
ime o e alua ion a he han o ime ’ > , as we assign hese a ibu es
now. The si ua ion can change; o cou se, John can la e o e o a ca , o
ins ance. In such a case, he sen ence is no ue.
Anyway, he piece o in o ma ion con eyed by he sen ence seems o be
incomple e, as one is emp ed o ask, “When will John go o B ussels?” I
is so because sen ences in he pas o u u e should con ain a cons i uen
e e ing o ime T → (οτ), he ime in e al when his o ha happened
o will happen. In such a case, he sen ence is associa ed wi h a p esuppo-
si ion ha he cu en ime is in he p ope ela ion wi h espec o T.
Roughly, i means ha o sen ences in u u e, comes be o e he end o
he e e ence ime T, while o sen ences in pas , comes a e T; i i is no
so, hen he p oposi ion deno ed by he sen ence has a u h- alue gap. Fo
ins ance, he sen ence “John will go o B ussels on Janua y 1s , 2023” can
be ue o alse ill Janua y 1s , 2023, 24:00. La e , i has no u h alue.
In ol ing p esupposi ion is easonable, o cou se. Imagine a si ua ion when
27 I am g a e ul o he anonymous e iewe o his ema k, which lead me o he
speci ica ion o an ac i i y ha is no ambiguous.
Speci ica ion o Agen s’ Ac i i ies in Pas , P esen and Fu u es 97
O ganon F 30 (1) 2023: 66–101
happened o will happen o be done oge he wi h he equency o he
ac i i y in he e e ence ime.
Fu he esea ch will concen a e on a s ill mo e de ailed analysis o
messages in di e en g amma ical enses, p esupposi ions o such messages,
and on dynamic aspec s o agen s’ ac i i ies. He e we will also apply he
esul s ob ained in he applica ion o Gen zen’s na u al deduc ion adjus ed
o TIL so ha hese me hods can be in eg a ed in o one in elligen sys em.
Acknowledgemen s
This esea ch has been suppo ed by he G an o SGS No. SP2022/123, VŠB-
Technical Uni e si y o Os a a, Czech Republic, “Applica ion o Fo mal Me hods
in Knowledge Modelling and So wa e Enginee ing V”, and by he Uni e si y o
Ox o d p ojec ‘New Ho izons o Science and Religion in Cen al and Eas e n Eu-
ope’ unded by he John Temple on Founda ion. I am g a e ul o wo anonymous
e iewe s whose commen s signi ican ly con ibu ed o imp o ing he quali y o he
pape .
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