Archive: December 3rd, 2008

Eric Mueller: Commonsense Reasoning

[Readings] (12.03.08, 3:44 pm)

This book is about an approach to commonsense reasoning that is implemented using formal logic. Mueller does not make the claim that humans make use of formal logic structures in understanding the physical world, but rather that this is a way for commonsense physical phenomena to be understood computationally. The approach does not replicate or even simulate the human method of cognition or understanding, but rather gives a formal account of relationships. Commonsense systems could be applied towards making predictions, performing diagnostics, or analysis within a simulated or artificial environment. Mueller uses classical first-order logic, and every element of commonsense reasoning takes the form of axioms that work within that space.

Mueller lays out a set of four assumptions that guide the rest of the investigation. These assumptions are certainly contestible, but they can be seen as a basis on which the rest of the work can be derived. (p. xx)

  • I assume, along with most cognitive scientists, that commonsense reasoning involves the use of representations and computational processes that operate on those representations.
  • I assume along with researchers in symbolic artificial intelligence, that the representations are symbolic.
  • I assume, along with researchers in logic-based artificial intelligence, that commonsense knowledge is best represented declaratively rather than procedurally.
  • I use the declarative language of many-sorted first order logic.

The formulation of commonsense reasoning accounts for a number of specific properties of real world objects. This contains the vocabulary and the elements that will be formalized into axioms of the commonsense reasoning logic. One noteworthy flaw within this is the element of perspective. For someone to have common sense, that individual must have a perspective. Mathematical logic in abstract does not have a perspective that is readily apparent. Even thought this logic can make commonsense conclusions, it still has a view from nowhere. (p. 7-8)

  1. Representation. The method must represent scenarios in the world and must represent commonsense knowledge about the world.
  2. Commonsense entities. The method must represent objects, agents, time varying properties, events, and time.
  3. Commonsense domains. The method must represent and reason about time, space, and mental states. The method must deal with object identity.
  4. Commonsense phenomena. The method must address the commonsense law of inertia, release from the commonsense law of inertia, concurrent events with cumulative and canceling effects, context-sensitive effects, continuous change, delayed effects, indirect effects, nondetermnistic effects, preconditions and triggered events.
  5. Reasoning. The method must specify processes for reasoning using representations of scenarios and representations of commonsense knowledge. The method must support default reasoning, temporal projection, abduction, and postdiction.

Commonsense logic originated with situation calculus as created by John McCarthy and Patrick Hayes in the 1960s. This was the inspiration for Robert Kowalski and Marek Sergot to develop event calculus, which is the method of Mueller’s investigation. The foundation of event calculus relies on the understanding of events and properties that change over time. Time dependent properties are called fluents, which could be typed variables or true-false values. Events are any occurrence that can happen within the world. Time in the event calculus is linear, and can be either discrete or continuous.

There are four main predicates that work on the event calculus (p. 11). Note that these are not elements of a “new” logical structure, but are rather constructions within the framework of first order logic.

  1. HoldsAt(f, t) represents that fluent f is true at timepoint t.
  2. Happens(e, t) represents that event e occurs at timepoint t.
  3. Initiates(e, f, t) represents that, if event e occurs at timepoint t, then fluent f will be true after t.
  4. Terminates(e, f, t) represents that, if event e occurs at timepoint t, then fluent f will be false after t.

Using these elements, many axioms can be declared. These define the ordering of time, how effects may be defined or triggered, how events may be preconditions, what cumulative effects are, what abnormal states are, and so on. These are elaborated in detail throughout the book. They work together to form a representation of commonsense reasoning within a domain. In addition to these axioms, a domain must include observations of the world’s properties at various times, and a narrative of the known events in the world (p. 35). Mueller gives a formal definition for a domain description (p. 37):

  • Positive effect axioms, negative effect axioms, release axioms, effect constraints, positive cumulative effect axioms, and negative cumulative effect axioms.
  • Event occurrence formulas, temporal ordering formulas (the narrative).
  • Trigger axioms, causal constraints, and disjunctive event axioms.
  • Cancellation axioms.
  • Unique names axioms.
  • State constraints, action precondition axioms, and event occurrence constraints.
  • Trajectory and antitrajectory axioms.
  • Observations.
  • Event calculus axioms.

This is an extensive list, but composed together it represents what would completely define a domain within the calculus. This is actually quite contestible when compared with human reasoning. Human reasoning is necessarily incomplete, and much of the logical formulations are never explicit. For the purposes of logical reasoning, it still seems somewhat rigid and inflexible. It is severely dependent on total objective knowledge. With missing or incorrect knowledge, the logic might be crippled.

Later on, Mueller gives a chapter on the Mental States of Agents. This too gives an external and objective perspective on the modeled phenomena. It necessarily has an external omnitient view inside the minds of the emotional agents. The ostensible goal of this is to develop a system which can reason about emotions, but that too depends on issues of understanding and perception. Agents themselves, as modeled, have beliefs, and thus are subject to some perspective, but the logic will reason about those beliefs without perspective.

Mueller first gives a version of the Beliefs, Desires, and Intentions framework (listed as Beliefs, Goals, and Plans). This gives a clear logical account for conclusions that may be derived from BDI agents and environments. This reasoning is still very complex, but could be made more rapid though computational implementation.

Next, there is a logical formulation of the emotion theory developed by Ortony, Clore, and Collins. The formulation uses the system of eliciting conditions. The goal is to make logical conclusions about the emotions of agents when events occur. This work creates definitions for the predicates, Joy(a, e), meaning that agent a is joyful about event e, and goes to more complicated predicates such as Appreciation(a1, a2, e), which means that agent a1 is appreciative of agent a2 for performing action e. Following this is a large series of axioms which formally defines the relationships between the various predicates of deirability, belief, joy, distress, hope, resentment, and so on.

Default reasoning is constructed using vanilla 1st order logic, not with any messy nonmonotonic logic, or probabilistic reasoning. The perspective here relies on a total account of abnormal conditions, and a total knowledge of the states of objects. This formulation is especially problematic from a sociological perpective because of its emphasis on the cases of normality. An example given is that apples are red, unless some abnormal condition applies, such as that the apple is a Granny Smith, or is rotten. Of course, the claim of normal or default conditions is highly contestible, and an architecture that encourages defaults could lead to problematic assumptions.

Reading Info:
Author/EditorMueller, Eric
TitleCommonsense Reasoning
ContextMuller describes event calculus, which can be used for describing states and knowledge
Tagsai, specials
LookupGoogle Scholar, Google Books, Amazon