Languages 2022, 7, 217 10 of 23
Tableau 3. Symmetrical optimization in French, German, and Dutch (example (12)).
Prod: E-R,S *PST *PFV
E-S ↔ PST
E-R ↔ PFV
PST *
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
Languages 2022, 7, x FOR PEER REVIEW 8 of 24
Bidirectional Optimality Theory is a framework that models simultaneous
optimization of form and meaning, thus leading to optimal form-meaning pairs, instead
of just optimal forms on the basis of input meanings, or just optimal interpretations on the
basis of input forms (Hendriks et al. 2010). When a language has two available forms for
two related interpretations, there are four form-meaning pairs that participate in the
bidirectional OT competition, of which two pairs will win. These winning pairs are both
called superoptimal. When a language has four related temporal meanings, E,R,S, E-R,S,
E,R-S, and E-R-S, and four related tenses, i.e., present tense, simple past, present perfect,
and pluperfect, we obtain four superoptimal pairs relating each tense to one meaning.
This is shown in Tableau 1 (constraint violations are indicated with *). Tableau 1 presents
a global analysis of the competition between these four meanings in a language with these
four tenses (present tense, simple past, present perfect, and pluperfect) on the basis of the
four constraints given above. Ranking the constraints would not alter the outcome of the
bidirectional optimization. Therefore, we leave them unranked with respect to each other.
To indicate this, the lines between the constraints are dotted instead of solid in the tableau.
The superoptimal (winning) pairs in Tableau 1 are indicated by the sign .
Tableau 1. Bidirectional optimization of tenses.
*PFV *PST E-S ↔ PST E-R ↔ PFV
PRS, E,R,S
PRS, E-R,S * *
PRS, E,R-S *
PRS, E-R-S * *
PST, E,R,S * *
PST, E-R,S * *
PST, E,R-S *
PST, E-R-S * *
PRF, E,R,S * *
PRF, E-R,S * *
PRF, E,R-S * * *
PRF, E-R-S * *
PLUP, E,R,S * * * *
PLUP, E-R,S * *
PLUP, E,R-S * * *
PLUP, E-R-S * *
Tableau 1 shows that the first superoptimal pair is the pair that associates present
tense to the E,R,S meaning, because this form-meaning pair does not violate any of the
four constraints. This superoptimal pair blocks all other pairs with E,R,S as a meaning,
and all other pairs with PRS as a form. The second round of bidirectional optimization
results in the superoptimal pair that links the simple past to the meaning E,R-S, as this
pair only violates the markedness constraint that penalizes past tense marking (*PST). The
third and fourth superoptimal pairs combine the present perfect with the meaning E-R,S
(violating one markedness and one faithfulness constraint), and the pluperfect with the
meaning E-R-S, violating the two markedness constraints, but satisfying the two
faithfulness constraints.
Note that, irrespective of the ranking between the two markedness constraints *PFV
and *PST, bidirectional optimization results in three superoptimal pairs of form and
meaning for reference to eventualities in the past, indicated by the sign in Tableau 1.
This accounts for the fact that, in the languages under consideration in this article, the core
meanings of simple past and present perfect are E,R-S and E-R,S respectively, whereas the
pluperfect is linked to E-R-S. Although this is a welcome result, bidirectional optimization
PRF *
*
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
E-R,S
E,R-S * *
Similarly, the unidirectionally optimal form to refer to past eventualities in French,
German, and Dutch is the present perfect, and as such it may sometimes be used to express
an E,R-S reading, even though this pair is not the winner of bidirectional optimization.
This is illustrated by Schaden’s (2009) examples in (11) above. Again, the possibility to use
the unmarked present perfect for another reading is only allowed if the unidirectionally
optimal form yields the right interpretation. This again depends on the context. We assume
that the temporal adverbial signals an E,R-S reading in (11) above. The analysis is illustrated
in Tableau 4.
Tableau 4. Asymmetrical optimization in French, German, and Dutch (example (11)).
Prod: E,R-S *PST *PFV
E-S ↔ PST
E-R ↔ PFV
Languages 2022, 7, x FOR PEER REVIEW 8 of 24
Bidirectional Optimality Theory is a framework that models simultaneous
optimization of form and meaning, thus leading to optimal form-meaning pairs, instead
of just optimal forms on the basis of input meanings, or just optimal interpretations on the
basis of input forms (Hendriks et al. 2010). When a language has two available forms for
two related interpretations, there are four form-meaning pairs that participate in the
bidirectional OT competition, of which two pairs will win. These winning pairs are both
called superoptimal. When a language has four related temporal meanings, E,R,S, E-R,S,
E,R-S, and E-R-S, and four related tenses, i.e., present tense, simple past, present perfect,
and pluperfect, we obtain four superoptimal pairs relating each tense to one meaning.
This is shown in Tableau 1 (constraint violations are indicated with *). Tableau 1 presents
a global analysis of the competition between these four meanings in a language with these
four tenses (present tense, simple past, present perfect, and pluperfect) on the basis of the
four constraints given above. Ranking the constraints would not alter the outcome of the
bidirectional optimization. Therefore, we leave them unranked with respect to each other.
To indicate this, the lines between the constraints are dotted instead of solid in the tableau.
The superoptimal (winning) pairs in Tableau 1 are indicated by the sign .
Tableau 1. Bidirectional optimization of tenses.
*PFV *PST E-S ↔ PST E-R ↔ PFV
PRS, E,R,S
PRS, E-R,S * *
PRS, E,R-S *
PRS, E-R-S * *
PST, E,R,S * *
PST, E-R,S * *
PST, E,R-S *
PST, E-R-S * *
PRF, E,R,S * *
PRF, E-R,S * *
PRF, E,R-S * * *
PRF, E-R-S * *
PLUP, E,R,S * * * *
PLUP, E-R,S * *
PLUP, E,R-S * * *
PLUP, E-R-S * *
Tableau 1 shows that the first superoptimal pair is the pair that associates present
tense to the E,R,S meaning, because this form-meaning pair does not violate any of the
four constraints. This superoptimal pair blocks all other pairs with E,R,S as a meaning,
and all other pairs with PRS as a form. The second round of bidirectional optimization
results in the superoptimal pair that links the simple past to the meaning E,R-S, as this
pair only violates the markedness constraint that penalizes past tense marking (*PST). The
third and fourth superoptimal pairs combine the present perfect with the meaning E-R,S
(violating one markedness and one faithfulness constraint), and the pluperfect with the
meaning E-R-S, violating the two markedness constraints, but satisfying the two
faithfulness constraints.
Note that, irrespective of the ranking between the two markedness constraints *PFV
and *PST, bidirectional optimization results in three superoptimal pairs of form and
meaning for reference to eventualities in the past, indicated by the sign in Tableau 1.
This accounts for the fact that, in the languages under consideration in this article, the core
meanings of simple past and present perfect are E,R-S and E-R,S respectively, whereas the
pluperfect is linked to E-R-S. Although this is a welcome result, bidirectional optimization
PST *
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
PRF *
*
*
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S *
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
E,R-S *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S *
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
E,R-S
Although the simple past is the bidirectionally optimal form for the E,R-S interpreta-
tion, the present perfect can be used as a unidirectionally optimal form in (11), as long as the
form yields the intended interpretation in the context (otherwise, FIT would be violated).
In English and Spanish, the simple past is the unidirectionally and bidirectionally form in
this context, as shown in Tableau 5.
Tableau 5. Symmetrical optimization in English and Spanish (example (11)).
Prod: E,R-S *PFV *PST
E-S ↔ PST
E-R ↔ PFV
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
Languages 2022, 7, x FOR PEER REVIEW 8 of 24
Bidirectional Optimality Theory is a framework that models simultaneous
optimization of form and meaning, thus leading to optimal form-meaning pairs, instead
of just optimal forms on the basis of input meanings, or just optimal interpretations on the
basis of input forms (Hendriks et al. 2010). When a language has two available forms for
two related interpretations, there are four form-meaning pairs that participate in the
bidirectional OT competition, of which two pairs will win. These winning pairs are both
called superoptimal. When a language has four related temporal meanings, E,R,S, E-R,S,
E,R-S, and E-R-S, and four related tenses, i.e., present tense, simple past, present perfect,
and pluperfect, we obtain four superoptimal pairs relating each tense to one meaning.
This is shown in Tableau 1 (constraint violations are indicated with *). Tableau 1 presents
a global analysis of the competition between these four meanings in a language with these
four tenses (present tense, simple past, present perfect, and pluperfect) on the basis of the
four constraints given above. Ranking the constraints would not alter the outcome of the
bidirectional optimization. Therefore, we leave them unranked with respect to each other.
To indicate this, the lines between the constraints are dotted instead of solid in the tableau.
The superoptimal (winning) pairs in Tableau 1 are indicated by the sign .
Tableau 1. Bidirectional optimization of tenses.
*PFV *PST E-S ↔ PST E-R ↔ PFV
PRS, E,R,S
PRS, E-R,S * *
PRS, E,R-S *
PRS, E-R-S * *
PST, E,R,S * *
PST, E-R,S * *
PST, E,R-S *
PST, E-R-S * *
PRF, E,R,S * *
PRF, E-R,S * *
PRF, E,R-S * * *
PRF, E-R-S * *
PLUP, E,R,S * * * *
PLUP, E-R,S * *
PLUP, E,R-S * * *
PLUP, E-R-S * *
Tableau 1 shows that the first superoptimal pair is the pair that associates present
tense to the E,R,S meaning, because this form-meaning pair does not violate any of the
four constraints. This superoptimal pair blocks all other pairs with E,R,S as a meaning,
and all other pairs with PRS as a form. The second round of bidirectional optimization
results in the superoptimal pair that links the simple past to the meaning E,R-S, as this
pair only violates the markedness constraint that penalizes past tense marking (*PST). The
third and fourth superoptimal pairs combine the present perfect with the meaning E-R,S
(violating one markedness and one faithfulness constraint), and the pluperfect with the
meaning E-R-S, violating the two markedness constraints, but satisfying the two
faithfulness constraints.
Note that, irrespective of the ranking between the two markedness constraints *PFV
and *PST, bidirectional optimization results in three superoptimal pairs of form and
meaning for reference to eventualities in the past, indicated by the sign in Tableau 1.
This accounts for the fact that, in the languages under consideration in this article, the core
meanings of simple past and present perfect are E,R-S and E-R,S respectively, whereas the
pluperfect is linked to E-R-S. Although this is a welcome result, bidirectional optimization
PST *
PRF *
*
*
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S *
Languages 2022, 7, x FOR PEER REVIEW 9 of 24
cannot account for Schaden’s puzzle, namely, the difference between Spanish and English
on the one hand, and French, German, and Dutch on the other. We argue that the
difference between these languages is the result of a different ranking between the two
markedness constraints *PFV and *PST. This provides an opportunity to model Schaden’s
observations in an asymmetric model of bidirectional optimization, in which the outcome
of production is constrained by interpretation (de Swart 2011).
In order to account for Schaden’s (2009) patterns of ‘default’ tenses, we propose that
in English and Spanish, *PFV outranks *PST, whereas in French, German, and Dutch, *PST
outranks *PFV. Because of these different rankings, the simple past will be the unmarked
(optimal) form to refer to past eventualities in Spanish and English, whereas the present
perfect will be the unmarked (optimal) form to refer to past eventualities in French,
German, and Dutch.
If *PFV ranks above *PST, which we argue is the case in Spanish and English, the
unmarked form may win the competition in an asymmetric OT derivation, as long as the
unmarked form does yield the right (intended) interpretation. This pattern is reminiscent
of other linguistic phenomena, such as differential object marking (de Swart 2011), where
a marked form is used to obtain a marked interpretation, whereas the unmarked (default)
form can have both an unmarked and a marked reading (de Hoop et al. 2004). If the
context allows the hearer to arrive at the marked reading in the absence of the marked
form, the speaker may suspend the use of the marked form for economy reasons
(Hendriks et al. 2010; Lestrade and de Hoop 2016). Whether this is the case depends on
the context. Recall example (12), in which the context (Archimedes in the bath) facilitates
the E-R,S-meaning, because the relevance of the finding at speech time is more important
than the fact that the finding happened in the past. That is to say, Archimedes is not telling
a story about how he found something in the past (E,R-S). Rather, Archimedes is in a state
of excitement because of what he has just discovered. Hence, the use of a present perfect
does not seem necessary to arrive at the intended meaning E-R,S, at least not in English
and Spanish. If Archimedes had uttered Ik vond het! ‘I found it’ in Dutch, however, this
would force an E,R-S reading, as if he were telling a story. This is not the case in English
and Spanish, but to allow the speaker to use the simple past in English and Spanish, it
must be checked whether this unmarked form would result in the right interpretation. For
this, we use a general meaning constraint, called FIT, that requires an interpretation to fit
the context (Zwarts 2004):
• FIT: The interpretation should fit the (linguistic or extra-linguistic) context.
In (12) the given context is in favor of an E-R,S-interpretation, and an E,R-S meaning
would violate FIT. This means that a speaker of Spanish or English can choose the
unmarked (unidirectionally optimal) simple past here, even if it is not the bidirectionally
optimal form (de Swart 2011). This is illustrated in Tableau 2.
Tableau 2. Asymmetrical optimization in English and Spanish (example (12)).
Prod: E-
R,S
*PFV *PST E-S ↔ PST E-R ↔ PFV
PST * *
PRF * *
Int: PST FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S *
Int: PRF FIT PST ↔ E-S PFV ↔ E-R
E-R,S
E,R-S * *
E,R-S
Hendriks et al. (2010) discuss several possible architectures of bidirectional optimiza-
tion, including asymmetrical models. Bidirectional optimization crucially hinges upon
the existence of two available related forms for two closely related meanings (three forms
for three meanings, four forms for four meanings, etc.). If only one meaning is available
for two related forms, then the speaker can choose between the two forms, but if only
one form exists for two meanings, then this form has to be ambiguous (de Hoop et al.
2004). Lestrade et al. (2016) show how unidirectional constraints can be derived from
generalizations over multiple bidirectional optimization processes. Therefore, if or when