Abstract
We utilize higher order automated deduction technologies for the logical analysis of natural-language arguments. Our approach, termed computational hermeneutics, is grounded on recent progress in the area of automated theorem proving for classical and nonclassical higher order logics, and it integrates techniques from argumentation theory. It has been inspired by ideas in the philosophy of language, especially semantic holism and Donald Davidson’s radical interpretation; a systematic approach to interpretation that does justice to the inherent circularity of understanding: the whole is understood compositionally on the basis of its parts, while each part is understood only in the context of the whole (hermeneutic circle). Computational hermeneutics is a holistic, iterative approach where we evaluate the adequacy of some candidate formalization of a sentence by computing the logical validity of (i) the whole argument it appears in and (ii) the dialectic role the argument plays in some piece of discourse.
Christoph Benzmüller: Funded by VolkswagenStiftung under grant CRAP: Consistent Rational Argumentation in Politics.
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Notes
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The notion of reflective equilibrium has been initially proposed by Goodman (1983) as an account for the justification of the principles of (inductive) logic and has been popularized years later in political philosophy and ethics by Rawls (2009) for the justification of moral principles. In Rawls’ account, reflective equilibrium refers to a state of balance or coherence between a set of general principles and particular judgments (where the latter follow from the former). We arrive at such a state through a deliberative give-and-take process of mutual adjustment between principles and judgments. More recent methodical accounts of reflective equilibrium have been proposed as a justification condition for scientific theories (Elgin 1999) and objectual understanding (Baumberger and Brun 2016).
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As described below, using the technique of semantical embeddings (Benzmüller and Paulson 2013) (cf. also Benzmüller 2019 and the references therein) allows us to work with several different nonclassical logics (modal, temporal, deontic, intuitionistic, etc.) while reusing existing higher order reasoning infrastructure.
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The situation is obviously idealized, since as is well known, most of theorem-proving problems are computationally complex and even undecidable, so in many cases, a solution will take several minutes or just never be found. Nevertheless, as work in the emerging field of computational metaphysics (Fitelson and Zalta 2007; Rushby 2013; Benzmüller and Woltzenlogel Paleo 2014, 2016a; Benzmüller et al. 2017; Fuenmayor and Benzmüller 2017a) suggests, the lucky situation depicted above is not rare and will further improve in the future.
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The assessment presented here draws on previous work in Fuenmayor and Benzmüller (2017a) and particularly the more recent, invited paper (Benzmüller and Fuenmayor 2018), which present an updated analysis of Gödel’s and Scott’s modal variants (Gödel 2004; Scott 2004) of the ontological argument and illustrate how our method is able to formalize, assess, and explain those in full detail.
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See lines 4–5 in Fig. 4, where their definitions are provided for classical logic.
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The full flexibility of our framework is not illustrated to its maximum in this paper due to space restrictions. For example, for intuitionistic logic we would simply integrate the respective embedding presented in earlier work Benzmüller and Paulson (2010) to model intuitionistic support/attack relations.
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Fuenmayor, D., Benzmüller, C. (2019). Computational Hermeneutics: An Integrated Approach for the Logical Analysis of Natural-Language Arguments. In: Liao, B., Ågotnes, T., Wang, Y. (eds) Dynamics, Uncertainty and Reasoning. CLAR 2018. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-13-7791-4_9
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