Frame Semantics of Continuous Processes

Qualitative Process theory provides a formal representation for human-like models of continuous processes. However, qualitative reasoning systems frequently rely on hand-made models which inhibits expansion into new domains. A representation that unifies QP theory with natural language expressions would allow these systems to expand their models by reading and interaction, thus greatly increasing their flexibility. Prior research mapped qualitative process elements onto English language constructions, but did not connect the representations to existing frame semantic resources. Here we identify and classify QP language constituents through their instantiation in FrameNet frames to provide a unified semantics for linguistic and nonlinguistic representations of processes. We demonstrate that all core QP relations can map to FN, though larger QP evoking phrasal constructions do exist outside of this mapping. We conclude with a corpus analysis showing that these frames occur in natural text involving a variety of continuous processes. Introduction & Background Much of daily experience involves interacting with, and reasoning about, continuous processes. They can be common, such as coffee flowing into your mug, or they can be abstract, like economic growth. Despite the mathematical complexity of continuous processes, people rapidly generate predictions based on their mental models of these situations. Forbus’ (1984) qualitative process theory (QP) provides a formal language for representing mental models of these continuous systems. The theory benefits from being domain general and has significant predictive power. An important issue is bridging the gap between purely linguistic models and QP mental models, to provide a unified semantics. Doing so not only sheds light on the semantics of continuous phenomena, but also lays the groundwork for developing systems that can learn from and reason with natural language (McFate, Forbus, & Hinrichs, 2014). Kuehne (2004) developed QP frames, a frame semantic representation based on Fillmore et al’s (2001) FrameNet. This approach was revised and expanded by McFate et al (2014). While useful, both approaches suffered from limited coverage and did not connect QP frames to frame semantic resources more broadly. This paper further bridges that gap by providing a QP mapping of specific process types in FrameNet as well as their constraints, including limit points, which mark the boundaries of qualitative states. This in turn provides a broader coverage analysis of QP elements in English that also grounds them in process specific linguistic constructions. Qualitative Process Theory In QP theory, changes within a continuous system are always the result of processes. Causality starts with direct influences, which express the relationship between the rate of a process and the constrained quantity. A direct influence provides partial knowledge of a differential equation, where the set of direct influences must be combined to determine the derivative. Indirect influences propagate the direct effects of a process through the rest of a system by providing partial information about instantaneous (e.g. algebraic) causal relationships. Processes and their influences are represented by model fragments which describe the entities that participate in a process, the conditions under which instances of it are active, and what consequences hold when active. The conditions typically include ordinal relationships, which involve a quantity and one of its limit points QP theory provides a framework for representing mental models for many naturally occurring phenomena across a range of expertise. However, the incremental nature of language makes extracting complete QP models difficult. We turn to frame semantics to help provide the needed flexibility. Frame Semantics Semantic frames are conceptual schemas that relate lexical items in a sentence to their role in a semantic description (Fillmore, Wooters, & Baker, 2001). Fillmore et al’s (2001) FrameNet is a frame semantics for English. FrameNet frames are evoked by a frame-bearing lexical unit. The dependent structures in the sentence form arguments to that frame’s frame elements (FEs). For example, the Motion frame includes frame elements for the Source, Goal, and Theme. It is instantiated in a specific construction (a pairing of syntactic form and semantic meaning) by a frame evoking lexical unit (LU) such as the word fly in “The bird flew to Florida”. Here, the noun phrase (NP) subject fills the role of Theme and the prepositional phrase (PP), ‘to Florida’, fills the role of Goal. The specific grammatical instantiation of these roles is called a valence pattern for that lexical unit. Thus a simple transitive would have a valence pattern of an NP subject and an NP object. Two core inter-frame relationships in FrameNet are inheritance and sub-frame. A frame that inherits from a parent must have a corresponding frame element for each element of the parent and can introduce others. Inheritance can be partial or multiple (Baker, Fillmore & Cronin, 2003). Sub-frames allow FrameNet to represent complex scenarios as a sequence of smaller parts related through precedence. QP Language Kuehne (2004) recast QP theory in a frame-semantic representation to better handle compositionality in language. Quantity frames fill the argument slots of influence frames. The influences participate in quantity transfer descriptions and process frames which express the results and activation conditions of the process. This representation differs from FrameNet in that sub-frames in FrameNet are related through their role relations and frame-frame relations, instead of filling a frame element of the superordinate frame. Our representation benefits from compactness and allows us to define entire frames as FE arguments, though it is straightforward to transform them into FN conventions (e.g. Figure 1). Kuehne (2004) identified several syntactic patterns that instantiated QP frames, and used them to automatically extract QP frames from text, using Davidsonian lexical representations from Cyc KB 1 contents. This approach, while successful, was limited by the syntactic patterns in the controlled grammar and did not integrate into the language system more broadly. McFate et al (2014) extended this approach and introduced narrative functions to guide disambiguation (Tomai, 2009). This system’s coverage was limited by the coverage of Cyc’s semantic templates, and it also became evident that a finer-grained set of distinctions would be useful. Integrating QP frames with FrameNet helps solve both problems by providing valence patterns by frame type. It benefits frame semantics by providing rich representations for mental models. Unifying FrameNet with QP Frames Continuous Processes Continuous processes are process verbs and nominalized verbs in English. Since direct influences are only allowed within processes, we start with them. The direct influence (DI) frame has four required elements: constrained, constrainer, entity, and sign. The constrained and constrainer are both quantity frames. The entity is the process, and the sign indicates the direction of contribution for the rate. FrameNet has many frames that instantiate continuous processes and thus DIs. A straightforward mapping for these frames aligns QP elements to potential FrameNet elements. Figure 1, above, is an example of Fluidic_motion. It’s difficult to evaluate precisely how many frames in FrameNet instantiate a DI, but we can get a 1 http://www.cyc.com/platform/researchcyc Figure 1: QP frames for a sentence