T-AIF: Trichotomic Argument Interchange Format

• T-AIF is a formal graph-based argumentation model that integrates Logos, Ethos, and Pathos to capture reasoning, credibility, and emotional commitment.
• It uses directed, labeled multi-graphs to model entities, propositions, and scheme applications, incorporating fuzzy logic for graded semantic evaluations.
• The framework supports applications in profiling debate dynamics, trust network analysis, and NLP-driven extraction of argument and emotion in social interactions.

The Trichotomic Argument Interchange Format (T-AIF) is a formal, graph-based argumentation representation model that captures all three Aristotelian aspects of argument—Logos (reasoning), Ethos (credibility), and Pathos (emotional/strategic commitment)—within a single structured framework. Extending the Argument Interchange Format (AIF) and its variants, T-AIF enables fine-grained modeling of argument content, speakers, trust relationships, and expressive commitment levels, supporting both rich interactional and computational analysis of argumentation (Göttlinger et al., 2018).

1. Graph-Theoretic Meta-Model

T-AIF encodes argumentation as a directed, labeled multi-graph

$G = (V, E, \tau_V, \tau_E)$

where:

• $V$: node set, partitioned by node type;
• $E \subseteq V \times V$: edge set;
• $\tau_V: V \rightarrow \mathrm{NodeType}$: node type assignment;
• $\tau_E: E \rightarrow \mathrm{EdgeType}$: edge type assignment.

Node Types

Node Type	Denotation	Description
E-nodes	"Entities"	Agents, speakers, organizations
L-nodes	"Locutions"	Raw utterances or dialogue turns
I-nodes	"Illocutions"	Logical proposition content conveyed by L-nodes
SA-nodes	"Scheme App."	Applications of argument, conflict, or dialogue move

SA-nodes further specialize into RA-nodes (Rule Application), CA-nodes (Conflict Application), PA-nodes (Preference Application), TA-nodes (Transition Application), and YA-nodes (Illocutionary Force).

Edge Types

Edge Type	Source	Target	Weight	Role
reply	L-node	L-node	no	Dialogue turn structure
illocutionary (YA)	L-node	I-node	no	Links utterances to their propositional content (illocutionary force)
scheme-premise/exc.	I-node/SA	SA-node/I-node	no	Mapping premises/exceptions to scheme apps and conclusions
trust	E-node	E-node	yes	Weighted trust ($\tau(x, y) \in [0, 1]$)
commitment	E-node	I-node	yes	Weighted degree of actor’s commitment ($c(x, p) \in [0, 1]$)

2. Modeling Logos: Propositional and Structural Layer

Logos is modeled by AIF+ style networks connecting I-nodes (propositional content) via scheme applications and inference/attack/preference relations. Central definitions include:

Propositional and Scheme Infrastructure

• $P_i$: set of illocutionary propositions (I-nodes)
• $S = S_{att} \cup S_{sup}$: set of atomic schemes (attack/support)
• $as(s), es(s)$: arity and exception arity of scheme $V$0
• $V$1: admissible groundings (which premises/exceptions yield which conclusion)
• $V$2: fuzzy scheme interpretation

The Trichotomic Argumentation Framework (T-AF) is

$V$3

with semantics allowing for graded evaluations across attacks, supports, and scheme instantiations.

Example: “Position to Know” Scheme

Argumentative schemes can be defined with custom σ-functions. For instance, the "Position to Know" uses

$V$4

where $V$5 is fuzzy conjunction and $V$6 is fuzzy implication, following Łukasiewicz semantics (Göttlinger et al., 2018).

3. Ethos: Trust Networks Among Entities

Ethos is represented explicitly as a network of directed, weighted “trust” relations among E-nodes: $V$7 where $V$8 encodes the degree to which actor $V$9 trusts actor $E \subseteq V \times V$0.

Trust as Propositions and Aggregation

Each E-node may be viewed as a proposition (“$E \subseteq V \times V$1 is credible”). Trust can be injected into semantic labelings for reasoning consistency (via $E \subseteq V \times V$2). For indirect trust (e.g., trust across intermediaries), path-based aggregation such as

$E \subseteq V \times V$3

extracts the strongest bottleneck path.

4. Pathos: Commitment and Emotional Investment

Pathos is encoded as weighted “commitment” edges from each E-node (actor) to every I-node (proposition): $E \subseteq V \times V$4 where $E \subseteq V \times V$5 represents the degree of emotional or strategic commitment by $E \subseteq V \times V$6 to proposition $E \subseteq V \times V$7.

This layer enables formal modeling of different levels of actor investment, supporting fine-grained analysis of argumentation dynamics and actor motivation.

5. Unified Graph Model

Bringing together all modalities, the T-AIF unified graph comprises: $E \subseteq V \times V$8

Component	Description
E	Entities (agents, speakers)
L	Locutions (utterances)
I	Illocutions (propositions)
SA	Scheme applications (RA, CA, PA, TA, YA)

Edge sets:

• $E \subseteq V \times V$9: reply (L × L)
• $\tau_V: V \rightarrow \mathrm{NodeType}$0: illocutionary (L × I)
• $\tau_V: V \rightarrow \mathrm{NodeType}$1: scheme premises/exceptions (I × SA × {premise, exception})
• $\tau_V: V \rightarrow \mathrm{NodeType}$2: scheme conclusions (SA × I)
• $\tau_V: V \rightarrow \mathrm{NodeType}$3: trust (E × E, weighted)
• $\tau_V: V \rightarrow \mathrm{NodeType}$4: commitment (E × I, weighted)

An illustrative fragment (Brexit debate): an E-node [Entity B] has trust weight 0.8 to another speaker, and a commitment weight $\tau_V: V \rightarrow \mathrm{NodeType}$5 to the proposition "Brexit" (Göttlinger et al., 2018).

6. Semantics and Reasoning Patterns

T-AIF defines a graded, fuzzy extension of Dung-style semantics for the evaluation of arguments and commitments:

• Each proposition $\tau_V: V \rightarrow \mathrm{NodeType}$6 receives a real-valued label $\tau_V: V \rightarrow \mathrm{NodeType}$7.
• Each entity $\tau_V: V \rightarrow \mathrm{NodeType}$8 has a belief predicate $\tau_V: V \rightarrow \mathrm{NodeType}$9 quantifying the agreement between its own trust or commitment and the system labeling.

Attack, Support, and Labeling

Attack and support for proposition $\tau_E: E \rightarrow \mathrm{EdgeType}$0 under labeling $\tau_E: E \rightarrow \mathrm{EdgeType}$1 are defined as

$\tau_E: E \rightarrow \mathrm{EdgeType}$2

Defense, consistency, admissibility, completeness, groundedness, and preferred labelings are established analogously with fuzzy logic extensions (Göttlinger et al., 2018).

Actor-Specific Criteria and Metrics

Trichotomic extensions introduce further metrics:

• Similarity of actors ($\tau_E: E \rightarrow \mathrm{EdgeType}$3) via comparison of their labeling agreement,
• Agreement ($\tau_E: E \rightarrow \mathrm{EdgeType}$4), Rationality ($\tau_E: E \rightarrow \mathrm{EdgeType}$5), Justified Trust ($\tau_E: E \rightarrow \mathrm{EdgeType}$6), and Trust Compliance ($\tau_E: E \rightarrow \mathrm{EdgeType}$7), all defined via logical and fuzzy quantifiers.

A trust-sensitive evaluation procedure iterates on initial labels given by an actor’s commitments, updating via attack/support propagation, and measures compliance as a function of the above criteria.

7. Applications and Profiling

The multi-layered T-AIF representation supports diverse applications:

• Per-actor argumentation profiles: Rationality metrics, trust-compliance, and commitment tracking for each participant.
• Community structure: Actor similarity metrics ($\tau_E: E \rightarrow \mathrm{EdgeType}$8) enable clustering and detection of trust networks and echo chambers.
• Emotion- and source-aware recommendations: Pathos-driven tailoring of argument summaries, source evaluation, and identification of Ethos-based fallacies (e.g., Ad Hominem).
• Automated NLP-driven mining: Guiding natural language pipelines for extracting utterances (L-nodes), content (I-nodes), and quantifying argument, trust, and emotion from real-world data (such as social media).
• Customizable summaries: Trust-sensitive and commitment-sensitive debate presentations.

These capabilities position T-AIF as a formalism for both theoretical analysis and computational reasoning in multi-agent, socially-embedded, and affect-laden argumentation contexts (Göttlinger et al., 2018).