Generating Defeasible Knowledge Bases from Real-World Argumentations using D-BAS?

Abstract

d-bas is an open-source web tool for dialog-based online argumentation among non-expert human users [7]. In this work, we present dabasco, a d-bas module that allows to automatically export d-bas discussions, interpreted as defeasible knowledge bases, into formats of three well-established argumentation models: abstract Argumentation Frameworks, the ASPIC Framework, and Abstract Dialectical Frameworks.

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Introduction A major challenge of real world application of formal models of arguments is to establish a \pipeline" that allows to seamlessly map real argumentation data to formal model instances. A large body of research concentrates on developing methods to annotate natural language argumentations in order to identify their logical structure [ 13 ]. d-bas [ 7 ], as opposed to typical tools for online argumentation like forums and comment sections, has the upside of not generating unstructured bodies of natural language texts. Users can input text only in the form of short statements, which hold no internal logical structure. Logical relations between statements are given on a purely meta level using the Web interface. Therefore, d-bas discussions are automatically, naturally structured.

The purpose of this work is to present dabasco, a tool that utilizes d-bas as a source of structured argumentation data and allows to translate d-bas data into abstract Argumentation Frameworks [ 4 ], the ASPIC framework [ 3 ], and Abstract Dialectical Frameworks [ 2 ]. We brie y describe the d-bas data model, then give short de nitions of the target argumentation models that dabasco translates to, demonstrate the translations, and provide instructions on how to download and use dabasco. or a single negated argument as its conclusion. The argument represents the application of an inference rule which claims that the premise is a reason to believe the conclusion. Each user opinion holds information about which statements and arguments that user has accepted or rejected. For more detailed information, we refer to Krautho et al. [ 7 ].

Example 1 (The Nixon Diamond as a d-bas discussion). To illustrate the syntax of a d-bas discussion, we formalize the well-known Nixon diamond as a d-bas discussion. Each statement and inference rule is given with its corresponding ID, where rule IDs have a leading \r" to avoid confusion.

Statements:

Inference Rules: 1 \Nixon is a paci st" 2 \Nixon is a quaker" 3 \Nixon is a republican" r1 \Nixon is a paci st" because \Nixon is a quaker". r2 \Nixon is not a paci st" because \Nixon is a

republican".

In Example 1, the two arguments that apply inference rules r1 and r2, respectively, rebut each other|they have con icting conclusions. Following Prakken [ 8 ], d-bas allows two more variants of attack among arguments: undermining attacks, where an argument's conclusion contradicts a premise statement of another argument, and undercutting attacks, where an argument has the negated identi er of another argument as its conclusion, i.e., directly attacks the inference rule applied in that other argument. To showcase these types of argument attack, we slightly extend Example 1 by the following ( ctitious) statements and arguments.

Example 1 (continued). We add inference rules r3 and r4 with two new statements 4 and 5 to the discussion: r3 \Nixon is not a quaker (:2)" because \Nixon converted to Catholicism (4)". r4 Rule r2 does not apply because "there are paci st republicans (5)". Disregarding the content of the statements yields the following abstract representation of the discussion, which will be used as a running example throughout the paper: statements = f1; 2; 3; 4; 5g inf erences = fr1 : [ 2 ] ) 1; r2 : [ 3 ] ) :1; r3 : [ 4 ] ) :2; r4 : [ 5 ] ) :r2g A d-bas discussion can be seen as a defeasible knowledge base (DKB) [ 3 ]. A DKB consists of a set of literals (closed under negation) and a set of inference rules that indicate logical relations between literals. Inference rules have a body and a head, where the body is a conjunction of literals and the head is a single literal, indicating that the body infers the head. A rule body may be empty, in which case there is no precondition to infer the head. The inference rules are often divided into strict and defeasible rules, where the head of a strict rule is always true if the body is true, whereas there may be circumstances where the head of a defeasible rule is not true even when its body is.

A d-bas discussion can be mapped to a DKB by identifying d-bas statements and their negations with literals and d-bas inference rules as defeasible inference rules. Since all arguments in d-bas are user-generated, there are no strict rules. To cover undercutting attacks, it is also required to allow rule identi ers as heads of defeasible rules, either by including rule identi ers in the set of literals or by directly allowing meta-level inferences. Further, user opinions can be used as a source for assumptions. Some argumentation systems explicitly model assumptions (e.g., the ASPIC framework [ 3 ]). In other systems, they can be implemented in the form of strict or defeasible rules with an empty body and the literal itself as the head. 3

Translations d-bas in itself is not restricted to a speci c normative interpretation, since all data is created by subjective users. This allows to interpret d-bas data in many di erent ways. dabasco currently implements translations of d-bas discussions to Argumentation Framework (AF), ASPIC, and Abstract Dialectical Framework (ADF) representations. Both the ASPIC and the ADF translation evaluate a single user opinion in the context of the dicussion by using it as a source for assumptions. The AF translation does not employ a user opinion and therefore produces an \objective" representation of the discussion. 3.1 An Argumentation Framework (AF) is a pair hA; Ri where A is a nite set of arguments and R A A is a binary attack relation on the arguments. Wyner et al. [ 12 ] proposed a method to translate defeasible knowledge bases to abstract AFs, which was implemented by Strass [ 11 ] for standard DKBs. dabasco provides an implementation that, in addition, covers the undercutting inference rules which are possible in d-bas discussions, without encoding inference rule identi ers as additional literals: in the translation, each argument representing an undercutting rule simply attacks its target argument. Other than that, the translation implemented in dabasco is exactly that of Wyner et al.|for a description, please refer to the original paper. dabasco produces AFs in ASPARTIX syntax [ 5 ] that can be directly fed into most existing AF solvers. Example 2. Figure 1 displays the argumentation framework obtained by translating the discussion from Example 1. The generated AF has 34 preferred extensions. All arguments are credulously acceptable and none are skeptically acceptable for the preferred semantics, indicating that all statements can be defended and all rules can be activated. 3.2 An Abstract Dialectical Framework (ADF) is a triple D = (S; L; C), where S is a set of statements, L S S is a set of directed links between statements, :2

2 r2

r3 :3 3 r4 :4 4 :5 5 and C = fCsgs2S is a set of acceptance conditions for each statement. Each acceptance condition Cs can be represented as a boolean formula over the acceptance status of all parents (with respect to L) of s. dabasco implements a translation of a d-bas discussion including a single user opinion to an ADF following a translation proposed by Strass [ 10 ]|again, we refer to the original paper for details. dabasco uses an extended DKB for the translation: for each accepted or rejected statement in the given user opinion, a bodyless strict rule is added which asserts that acceptance/rejection. These strict rules enforce the user opinion in the ADF. Without such a starting point for reasoning, no acceptance for any statement can be derived and all inference rules remain trivially inactive, because their premises do not hold. Since d-bas discussions hold no facts, we gured user opinions to be the most reasonable source for such \grounded" knowledge. dabasco produces ADFs in a clause-based format suitable to be used as input for the DIAMOND [ 6 ] and YADF [ 1 ] solvers.

Example 3. Consider a user opinion in which statements 3 and 4 are accepted and statement 5 is rejected. The following acceptance functions are generated when applying the ADF translation to the discussion from Example 1 using this user opinion, where si, ij and ak encode statement i, inference rule j and user assumption k, respectively, and a leading n indicates negation:

Cs1 = :Cns1 ^ Ci1 Cns1 = :Cs1 ^ Ci2 Cs2 = false Cns2 = :Cs2 ^ Ci3 Cs3 = :Cns3 ^ Ca3 Cns3 = false Cs4 = :Cns4 ^ Ca4 Cns4 = false Cs5 = false Cns5 = :Cs5 ^ Ca5

Ci1 = :Cns1 ^ :Cni1 ^ Cs2 Cni1 = :Ci1 Cni2 = :Ci2 Cni3 = :Ci3 Cni4 = :Ci4 Ci2 = :Cs1 ^ :Cni2 ^ Cs3 Ci3 = :Cs2 ^ :Cni3 ^ Cs4 Ci4 = :Ci2 ^ :Cni4 ^ Cs5

Ca3 = true Cna3 = :Cs3 ^ :Cna3 Ca4 = true Cna4 = :Cs4 ^ :Cna4 Ca5 = true

Cna5 = :Cns5 ^ :Cna5 model 4 false true true false false true false false true true true model 1 model 2

model 3 Cs1 undecided undecided undecided undecided Cs2 Cs3 Cs4 Cs5 Ci1 Ci2 Ci3 Ci4 Ca3 Ca4 Ca5 false true true false false false true false true true true false false true true false false true true false true true true true true false false false false false true true true

The ADF has the following four preferred models (undecided indicates cases where both an ADF statement and its negation are rejected):

Statements 1 and 2 are both rejected in two models and undecided in two models. Statements 3 and 4 are accepted in all models and statement 5 is rejected in all models (in compliance with the user opinion). Rules r1 and r4 are inactive in all models, and rules r2 and r3 are both active in two models. The ASPIC framework is a very powerful formalism that allows to directly encode DKBs. It is expressive enough to represent all features of a d-bas discussion without the need for a translation. dabasco generates ASPIC instantiations that are formatted as input for the TOAST online ASPIC solver [ 9 ]. Example 4. We export the extended Nixon example with the same user opinion as in the previous example. TOAST creates ve arguments: "A1 : 3"; "A2 : 4"; "A3 : 5"; "A4 : A2 ) 2"; "A5 : A1 ) 1" It produces a single preferred extension in which statements 3 and 4 are acceptable and statements 1, 2 and 5 are not. dabasco is available for download at https://github.com/hhucn/dabasco. It requires python 3 to run. A full guide for setup and use is included in the repository, along with a small mockup app that serves example d-bas data and allows to test dabasco's features without running d-bas. All Examples in this paper can be veri ed using discussion 2 and user 1 from the mockup app. dabasco is published under the MIT license and can be freely used and distributed.

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