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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>HLC</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>for human-like coordination systems.</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Eugene Philalithis</string-name>
          <email>E.Philalithis@ed.ac.uk</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="editor">
          <string-name>Reasoning, Comprehensibility, Explainable AI, Psycholinguistics</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>School of Informatics, University of Edinburgh</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>School of Philosophy, Psychology &amp; Language Sciences, University of Edinburgh</institution>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>3</volume>
      <fpage>28</fpage>
      <lpage>30</lpage>
      <abstract>
        <p>Recent work in explanatory machine learning highlights the value of symmetry between human and AI contributions in collaborative settings, in the form of a 'cognitive window' of optimal complexity that the AI collaborator must aim for. In this short paper, I argue the cognitive window is potentially mediated by processing styles, some fast and some slow, which the AI must also model to achieve the right 'handshake' with a human agent. I then consider some basic consequences of this added dimension.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Asymmetry</title>
      <p>One of the great natural ambitions of AI research is the creation of systems that can collaborate,
take instructions from, learn from and even teach human partners in nuanced and intuitive ways
that mirror how humans themselves collaborate, instruct, learn and teach. The behavioural
symmetry between such (putative) human-like coordination systems, and real human action and
decision-making, would allow them to replace human collaborators in many of these domains.</p>
      <p>
        However, when treating coordination as a reasoning problem, an asymmetry exists between
human and artificial agents, in the resources they each have available to reason with. All other
things being equal, AI systems comfortably outpace the human capacity for storing information
in working memory (cf. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]) and for computing optimal solutions based on that information; a
capacity evidenced by famous AI victories in chess [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], Go [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ] and Starcraft [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. As a result,
human performance is physically bounded in ways AI system performance is not. Artificial
systems must adjust to this asymmetry to work with, teach, or substitute human collaborators.
      </p>
      <p>
        Recent work in explanatory machine learning acknowledges and explores this asymmetry,
making the case for a ‘cognitive window’ of appropriate complexity - neither too high nor too
low - where an AI system positively contributes to human performance in an interactive game
[
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. AI contributions either overly complex or not complex enough can harm instead of help.
This cognitive window is defined by appeal to the reasoning capacity needed to fully represent
a problem: e.g. the memory cost of inferring and then implementing a winning move in a game.
      </p>
      <p>In this paper, I use the empirical literature to motivate the further dimension of matching
collaborators’ style of solution in tandem with its complexity. I call this the handshake problem.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Coordination, Fast and Slow</title>
      <p>
        A basic empirical intuition behind human reasoning - well-encapsulated in the nutshell of
‘thinking, fast and slow’ [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] - is redundancy for the sake of eficiency. When responding to
a wide array of challenges and decisions, human agents reflexively apply diferent styles and
speeds of cognitive processing, to suit the urgency, complexity or familiarity of each application.
      </p>
      <p>
        Where a task is routine or (importantly) where cognitive resources are strained, such as when
judging the outcomes of uncertain processes, human agents rely on fast and cheap heuristics,
producing a well-recorded legacy of errors and shortcuts [
        <xref ref-type="bibr" rid="ref10 ref8 ref9">8, 9, 10</xref>
        ]. Conversely, slower processes
may support explicit reasoning, action monitoring, or incorporation of domain knowledge [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ].
      </p>
      <p>
        Precise theories of how ‘dual-process’ reasoning would be implemented in human cognition
remain contentious [
        <xref ref-type="bibr" rid="ref11 ref12">11, 12</xref>
        ]; and the architectural scope of which tasks would fall under which
side of such a division remains unclear and subject to debate [
        <xref ref-type="bibr" rid="ref13 ref14">13, 14</xref>
        ]. This is not a settled claim.
For that reason, my present focus is not on implementing dual-process reasoning in artificial
systems. Instead, this paper focuses on the methodological challenge of how computational
models represent human ability for dual-process theories, relative to a single-process theory;
and on the particular implications of this challenge for models of coordination and explanation.
      </p>
      <p>
        Echoing the ‘fast and slow’ intuition for individual reasoning, similar contrasts range over
coordination and joint problem solving. On the one hand, coordination has been successfully
analysed as a ‘game’ of rigorous reasoning over implications [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], over an explicitly represented
perceptual and knowledge domain known as common ground [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]. On the other hand,
parts of this representation and domain knowledge have been shown to fall of in relevance as
working memory load increases [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] [19] in a trade-of with cheaper processes, like the simple
repetition of past structure, which may sufice to establish coordination in many settings [ 20].
A familiar contrast is implied, between a slow and rigorous method, and a faster more basic one.
      </p>
      <p>The thrust of this lower-level pathway for coordination is that coordination may not often
be a problem of reasoning over implications, but a cheaper ‘mechanistic’ problem of having
on-the-fly expectations of the next move or utterance by copying the last one [ 21]. Coordination
problems that are hard to reason through may be easier for a process based on expectation and
repetition. When cheap output is often suficient explicit reasoning becomes a fallback [ 22][23].</p>
      <p>Taken on its own, the ‘fast and slow’ intuition already carries significant implications for the
cognitive window approach to human-like AI. When diferent styles of solution are available,
the cognitive window where a problem is tractable for human agents becomes relative to the
style. An inherently simpler problem, measured e.g. by Kolmogorov complexity [24], could be
slower to solve using a richer problem-solving style than a cheap one. A complex problem may
turn out easier to process than a problem of slightly smaller inherent complexity, which was
allocated to a cheaper style: the window moves along two dimensions. And for coordination in
particular this movement can be fatal due to the need for symmetry. I turn to this issue below.</p>
    </sec>
    <sec id="sec-3">
      <title>3. The Handshake Problem</title>
      <p>
        I have so far considered the asymmetry in human and AI problem-solving resources, addressed
by limiting AI contributions to a cognitive window; and then raised the issue of alternate
processing and representation styles as a factor in human reasoning. This analysis conflicts
with the definition of the cognitive window from [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], represented as a fixed measure of upper
and lower bounds of computational complexity, in two main ways. The most obvious is that
the real cognitive window may not be constant, even where the underlying problem remains
unchanged. The same complex theory may be included in the cognitive window for a rich
processing style, but be fully outside the cognitive window for some cheaper processing style.
As a result, the processing style must be modelled, and condition cognitive window boundaries.
      </p>
      <p>
        The less obvious conflict concerns any possible changes of processing style as a result of an
unfavourable cognitive window. That is: a theory is initially chosen, but is replaced with another
because of memory or other resource limitations. This wholesale shift is well-documented in
human behaviour for collaborative tasks [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] [25] as I discuss more below. In this case the AI
system aiming for a cognitive window must reject its initial style of solution to match a human.
      </p>
      <p>Taking both demands together, an AI system may need to model (i) the initial challenge
a human collaborator faces for processing a problem, and (ii) the style of processing chosen
as a result, and its own associated upper/lower bounds of acceptable complexity. This is the
handshake problem as illustrated in Figure 1. Like a human handshake, the lower level of the
problem uses simpler information (e.g. the trajectory of a moving hand, equivalent to inherent
complexity); whereas the higher level involves a demanding modelling objective (the style of
handshake to try). One consequence for collaborative problem-solving is that a high complexity
contribution by an AI system, using a style that does match their human collaborator, may be
more appropriate and understandable than a lower complexity contribution in a diferent style.</p>
      <p>For coordination problems in particular, including most forms of two-way communication,
where the objective may not be just to jointly solve a problem but also to align [21] the symbols,
signals or systems used, a missed handshake may be fatal to the outcome, not just suboptimal.
A significant consequence of this constraint is that, where the richer process is not selected by
a human collaborator, the best solution by the cheaper process may be the correct choice even
where that solution is wrong. That is: where the cheaper process cannot solve the problem
optimally, its best (wrong) solution could nonetheless be the one that an AI system must opt for.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Shortcuts</title>
      <p>A formal solution or specification of the handshake problem is outside the scope of this brief
paper. However, as with human reasoning itself, there are always possible shortcuts to consider.</p>
      <p>One such shortcut is to decide the processing style in advance of the coordination problem.
Where humans must necessarily rely on a priori reasoning, e.g. in virtual bargaining [26], or
where past human behaviour in the same task has been extensively sampled, there may be no
need for an AI system to model processing styles. If human participants only ever attempt a
known task, e.g. 7x7 Noughts and Crosses, with a consistent processing style, the handshake
problem disappears. This is an empirical solution to a computational problem, where domain
knowledge of processing styles would be obtained before building the AI system, and ‘baked in’.</p>
      <p>
        Another shortcut is to lean on the cheaper, routine solution to miscoordination already used
by human collaborators in noisier settings: namely rejection and replacement. In a range of
coordination contexts, including the maze game [25] [27] and games from the other similar
literatures (notably [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]), pairs of human players who fail to establish a ‘handshake’ simply
reject their collaborator’s contributions, until or unless a handshake is achieved with a more
comprehensible alternative. Where rejected, the initial solution, representation or signal is
thrown out and humans try again. An AI system could emulate this by cycling between outputs.
      </p>
      <p>This second shortcut would sidestep the problem of modelling a cognitive window relative
to a processing style, in favour of the more heuristic approach of presenting outputs within a
range of similarity and complexity, until some output is accepted by the human collaborator.</p>
      <p>Human responsiveness to even basic, automated clarification requests in the maze game [ 28]
suggests that a comprehensible reject-and-replace feedback loop could be a relatively simple step
to ensure for collaborative AI systems, in settings where coordination may be mission-critical.
This reject-and-replace loop could be refined with a better grasp of the links between rejected
contributions and their alternatives, to generate more diferent or more similar alternate output.</p>
      <p>
        For popular coordination problems over conceptual domains - e.g. geometrical images [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ],
navigating a maze [25], or comparing diferent maps [ 29]) - this may be closer at hand. Recent
work in explanatory AI uses domain knowledge to generate alternative examples which are
conceptually ‘near’ or ‘far’ from an initial example of relational concepts [30], including spatial
concept domains. A comparable approach could potentially ofer intuitive alternatives when
navigating spatial domains in coordination tasks, such as geometry, maze layout representations
or maps, in line with observed human strategies for repairing unsuccessful coordination [27].
      </p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>Throughout the above I have focused on the single and simple task of motivating the handshake
problem as an extension of the cognitive window approach to human-AI coordination, then using
ifndings from the empirical literature to challenge the existing definition and help refine it. This
contribution is thus intentionally auxiliary and exploratory - intended as a basis for discussion
toward the larger goal for more collaborative, comprehensible, and ultimately human-like AI.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>The author is grateful to three anonymous reviewers for recommendations and a key example.
[19] B. Keysar, D. J. Barr, J. A. Balin, J. S. Brauner, Taking perspective in conversation: The role
of mutual knowledge in comprehension, Psychological Science 11 (2000) 32–38.
[20] M. J. Pickering, S. Garrod, Toward a mechanistic psychology of dialogue, Behavioral and
brain sciences 27 (2004) 169–190.
[21] M. J. Pickering, S. Garrod, Alignment as the basis for successful communication, Research
on Language and Computation 4 (2006) 203–228.
[22] M. J. Pickering, S. Garrod, An integrated theory of language production and comprehension,</p>
      <p>Behavioral and brain sciences 36 (2013) 329–347.
[23] M. J. Pickering, S. Garrod, Understanding dialogue: Language use and social interaction,</p>
      <p>Cambridge University Press, 2021.
[24] A. N. Kolmogorov, On tables of random numbers, Sankhyā: The Indian Journal of Statistics,</p>
      <p>Series A (1963) 369–376.
[25] S. Garrod, A. Anderson, Saying what you mean in dialogue: A study in conceptual and
semantic co-ordination, Cognition 27 (1987) 181–218.
[26] J. Misyak, T. Noguchi, N. Chater, Instantaneous conventions: The emergence of flexible
communicative signals, Psychological science 27 (2016) 1550–1561.
[27] P. G. Healey, G. J. Mills, A. Eshghi, C. Howes, Running repairs: Coordinating meaning in
dialogue, Topics in cognitive science 10 (2018) 367–388.
[28] P. G. Healey, M. Purver, J. King, J. Ginzburg, G. J. Mills, Experimenting with clarification
in dialogue, in: Proceedings of the Annual Meeting of the Cognitive Science Society,
volume 25, 2003.
[29] A. H. Anderson, M. Bader, E. G. Bard, E. Boyle, G. Doherty, S. Garrod, S. Isard, J. Kowtko,
J. McAllister, J. Miller, et al., The HCRC map task corpus, Language and speech 34 (1991)
351–366.
[30] J. Rabold, M. Siebers, U. Schmid, Generating contrastive explanations for inductive logic
programming based on a near miss approach, Machine Learning 111 (2022) 1799–1820.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>N.</given-names>
            <surname>Cowan</surname>
          </string-name>
          ,
          <article-title>What are the diferences between long-term, short-term, and working memory?</article-title>
          , in: W. S. Sossin,
          <string-name>
            <given-names>J.-C.</given-names>
            <surname>Lacaille</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V. F.</given-names>
            <surname>Castellucci</surname>
          </string-name>
          , S. Belleville (Eds.),
          <source>Essence of Memory</source>
          , volume
          <volume>169</volume>
          of Progress in Brain Research, Elsevier,
          <year>2008</year>
          , pp.
          <fpage>323</fpage>
          -
          <lpage>338</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>N.</given-names>
            <surname>Tomašev</surname>
          </string-name>
          ,
          <string-name>
            <given-names>U.</given-names>
            <surname>Paquet</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Hassabis</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Kramnik</surname>
          </string-name>
          ,
          <article-title>Reimagining chess with AlphaZero</article-title>
          ,
          <source>Communications of the ACM</source>
          <volume>65</volume>
          (
          <year>2022</year>
          )
          <fpage>60</fpage>
          -
          <lpage>66</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>D.</given-names>
            <surname>Silver</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Huang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C. J.</given-names>
            <surname>Maddison</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Guez</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Sifre</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Van Den Driessche</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Schrittwieser</surname>
          </string-name>
          ,
          <string-name>
            <given-names>I.</given-names>
            <surname>Antonoglou</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Panneershelvam</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Lanctot</surname>
          </string-name>
          , et al.,
          <article-title>Mastering the game of Go with deep neural networks and tree search</article-title>
          ,
          <source>Nature</source>
          <volume>529</volume>
          (
          <year>2016</year>
          )
          <fpage>484</fpage>
          -
          <lpage>489</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>D.</given-names>
            <surname>Silver</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Schrittwieser</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Simonyan</surname>
          </string-name>
          ,
          <string-name>
            <surname>I. Antonoglou</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Huang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Guez</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T.</given-names>
            <surname>Hubert</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Baker</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Lai</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Bolton</surname>
          </string-name>
          , et al.,
          <article-title>Mastering the game of Go without human knowledge</article-title>
          ,
          <source>Nature</source>
          <volume>550</volume>
          (
          <year>2017</year>
          )
          <fpage>354</fpage>
          -
          <lpage>359</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>O.</given-names>
            <surname>Vinyals</surname>
          </string-name>
          , I. Babuschkin,
          <string-name>
            <given-names>W. M.</given-names>
            <surname>Czarnecki</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Mathieu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Dudzik</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Chung</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. H.</given-names>
            <surname>Choi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Powell</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T.</given-names>
            <surname>Ewalds</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Georgiev</surname>
          </string-name>
          , et al.,
          <article-title>Grandmaster level in starcraft ii using multi-agent reinforcement learning</article-title>
          ,
          <source>Nature</source>
          <volume>575</volume>
          (
          <year>2019</year>
          )
          <fpage>350</fpage>
          -
          <lpage>354</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>L.</given-names>
            <surname>Ai</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S. H.</given-names>
            <surname>Muggleton</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Hocquette</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Gromowski</surname>
          </string-name>
          , U. Schmid,
          <article-title>Beneficial and harmful explanatory machine learning</article-title>
          ,
          <source>Machine Learning</source>
          <volume>110</volume>
          (
          <year>2021</year>
          )
          <fpage>695</fpage>
          -
          <lpage>721</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>D.</given-names>
            <surname>Kahneman</surname>
          </string-name>
          , Thinking, fast and slow, Penguin,
          <year>2012</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>D.</given-names>
            <surname>Kahneman</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S. P.</given-names>
            <surname>Slovic</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Slovic</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Tversky</surname>
          </string-name>
          ,
          <article-title>Judgment under uncertainty: Heuristics and biases</article-title>
          , Cambridge university press,
          <year>1982</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>J. S. B.</given-names>
            <surname>Evans</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. E.</given-names>
            <surname>Over</surname>
          </string-name>
          ,
          <article-title>Rationality and reasoning</article-title>
          , Psychology Press,
          <year>2013</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>N.</given-names>
            <surname>Chater</surname>
          </string-name>
          , The Mind Is Flat:
          <article-title>The Remarkable Shallowness of the Improvising Brain</article-title>
          , Yale University Press,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>J. S. B.</given-names>
            <surname>Evans</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K. E.</given-names>
            <surname>Stanovich</surname>
          </string-name>
          ,
          <article-title>Dual-process theories of higher cognition: Advancing the debate</article-title>
          ,
          <source>Perspectives on psychological science 8</source>
          (
          <year>2013</year>
          )
          <fpage>223</fpage>
          -
          <lpage>241</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>M.</given-names>
            <surname>Osman</surname>
          </string-name>
          ,
          <article-title>An evaluation of dual-process theories of reasoning, Psychonomic bulletin</article-title>
          &amp; review
          <volume>11</volume>
          (
          <year>2004</year>
          )
          <fpage>988</fpage>
          -
          <lpage>1010</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>D. E.</given-names>
            <surname>Melnikof</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. A.</given-names>
            <surname>Bargh</surname>
          </string-name>
          ,
          <article-title>The mythical number two</article-title>
          ,
          <source>Trends in cognitive sciences 22</source>
          (
          <year>2018</year>
          )
          <fpage>280</fpage>
          -
          <lpage>293</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>J. S. B.</given-names>
            <surname>Evans</surname>
          </string-name>
          ,
          <article-title>Reflections on reflection: the nature and function of type 2 processes in dual-process theories of reasoning</article-title>
          ,
          <source>Thinking &amp; Reasoning</source>
          <volume>25</volume>
          (
          <year>2019</year>
          )
          <fpage>383</fpage>
          -
          <lpage>415</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>H. H.</given-names>
            <surname>Clark</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G. L.</given-names>
            <surname>Murphy</surname>
          </string-name>
          ,
          <article-title>Audience design in meaning and reference</article-title>
          , in: Advances in psychology, volume
          <volume>9</volume>
          ,
          <string-name>
            <surname>Elsevier</surname>
          </string-name>
          ,
          <year>1982</year>
          , pp.
          <fpage>287</fpage>
          -
          <lpage>299</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>H. H.</given-names>
            <surname>Clark</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E. F.</given-names>
            <surname>Schaefer</surname>
          </string-name>
          , Contributing to discourse,
          <source>Cognitive science 13</source>
          (
          <year>1989</year>
          )
          <fpage>259</fpage>
          -
          <lpage>294</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <given-names>H. H.</given-names>
            <surname>Clark</surname>
          </string-name>
          ,
          <string-name>
            <surname>D.</surname>
          </string-name>
          Wilkes-Gibbs,
          <article-title>Referring as a collaborative process</article-title>
          ,
          <source>Cognition</source>
          <volume>22</volume>
          (
          <year>1986</year>
          )
          <fpage>1</fpage>
          -
          <lpage>39</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <given-names>W. S.</given-names>
            <surname>Horton</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Keysar</surname>
          </string-name>
          ,
          <article-title>When do speakers take into account common ground?</article-title>
          ,
          <source>Cognition</source>
          <volume>59</volume>
          (
          <year>1996</year>
          )
          <fpage>91</fpage>
          -
          <lpage>117</lpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>