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Professor Vern R. Walker

Hofstra University School of Law
Hempstead, New York 11549   USA

The following is adapted from Vern R. Walker,
Discovering the Logic of Legal Reasoning, 35 Hofstra Law Review 1687, 1696-1701 (2007)
Copy of full text available for download in .pdf format


The legal rules identify those issues of fact that are relevant to proving the ultimate issue of fact. As the branches of the rule or implication tree extend downward, the terminal conditions at the end of each sub-branch (the last propositions in each chain) constitute the issues of fact that are relevant. In any particular case, various participants (such as private parties, prosecutors, or administrative staffs) produce evidence for the legal record, and use that evidence to try to prove or disprove those issues of fact. The factfinder’s role is evidence assessment or evaluation: deciding which evidence is relevant to which issues of fact, evaluating the probative value of the relevant evidence, and making findings of fact based on that evidence. The logic of evidence assessment, therefore, studies the methods and principles for the inferential aspects of the factfinder’s task. It explains the reasoning that a reasonable factfinder would use to determine the probative value of the evidence.

As in the case of rules, a basic building block of evidence evaluation is the proposition. The propositions that constitute the evidence can be called “evidentiary assertions,” or simply “assertions,” to distinguish them from the propositions that constitute rules. Examples of evidentiary assertions are statements made by testifying witnesses or statements contained in documents that are admitted into evidence. Although witnesses and documents provide many of the evidentiary assertions in a particular case, the factfinder formulates additional assertions that play a role in the reasoning — for example, a description of an evidentiary exhibit or of a witness’s demeanor. While legal authorities create the rules for categories of cases, the witnesses, the documents, and the factfinder create the evidentiary assertions in each particular case.

Although evidentiary assertions are propositions, and therefore capable of being either true or false, factfinders are permitted to assign them degrees of plausibility (“plausibility-values”) instead of truth- values. In evaluating any particular evidentiary assertion, the legal rules also allow the factfinder to select the scale of plausibility to use. For example, the factfinder might use an ordinal, five-valued plausibility scale for some evidentiary assertions (with values such as “highly plausible” / “somewhat plausible” / “undecided” / “somewhat implausible” / “highly implausible”) and an ordinal, seven-valued scale for other assertions (with values such as “highly plausible” / “very plausible” / “slightly plausible” / “undecided” / “slightly implausible” / “very implausible” / “highly implausible”). On rare occasions, circumstances might even warrant using mathematical probabilities, with real numbers between zero and one as possible values.

A reasonable factfinder would select a scale of plausibility that is appropriately precise, given both the reliability of the available evidence and the accuracy and reliability needed to make the relevant findings of fact. For example, a factfinder might have little confidence in assessing the credibility of a particular fact witness, and so evaluate that witness’s assertions on an ordinal scale having very few degrees of plausibility. Occasionally, however, an expert might persuade the factfinder that a causal system is so well understood (for example, DNA profiling) that the factfinder can evaluate assertions about it using mathematical probabilities. On the other hand, such precision may not be necessary to perform the factfinding task. In a legal proceeding whose findings are made by the preponderance standard of proof, the evaluative precision needed may be rather low, and an ordinal scale with a small number of values may be entirely adequate. The beyond-a-reasonable-doubt standard, however, probably requires greater evaluative precision in order to support a verdict.

Evidence evaluation poses some challenges for formulating a useful, normative logic. One challenge is explaining how we reason about “relevance” itself — how we decide to link particular evidentiary assertions to particular issues of fact. Another challenge is studying the logical properties of different plausibility scales, although we can learn lessons from the theories of scientific classification and measurement. A further challenge is combining the plausibility-values of numerous evidentiary assertions into a single plausibility-value for a particular conclusion. This is a complicated problem in law because factfinders must be able to integrate both non-expert and expert evidence into a single pattern of reasoning. The warrant for the non-expert evidence might be commonsense reasoning about an eyewitness’s perceptual abilities and credibility, while the warrant for the scientific evidence might be controlled laboratory experiments and epidemiological studies. In the end, the factfinder must reason from all of the relevant evidence to a particular finding of fact.

Ideally, we want to identify the patterns of default reasoning that are actually used in law. If such patterns could be formalized into “plausibility schemas,” they might furnish useful, normative models for factfinders. In logic, a “schema” is a formal linguistic pattern containing variables, so that appropriate substitutions for the variables create instances of the pattern. A “plausibility” schema is a pattern of default reasoning that, when instantiated, warrants the conclusion to be plausible. For example, the schemas of deductive logic (such as “modus ponens”), which necessarily preserve truth from premises to conclusion, also preserve plausibility from premises to conclusion. More useful in typical legal cases, however, would be schemas based on inductive or abductive logic, or derived from scientific methodologies or heuristics. The typical plausibility schema has an inverted tree structure similar to that of an implication tree, except that the logical operators connecting the lower-level assertions to the upper-level conclusion function on the plausibility-values of the evidence, instead of on the truth-conditions of rules. Such schemas formulate patterns of plausible reasoning that warrant drawing provisional conclusions, which then remain subject to re-evaluation. Identifying those plausibility schemas that are actually used in legal factfinding will require empirical research into the reasoning patterns of judges, administrative officers, and expert agencies.

When a legal proceeding begins, the applicable legal rules identify all of the issues of fact that may be relevant. The factfinder then links the legally available evidentiary assertions to those issues of fact, using as heuristics those patterns of default reasoning familiar to the factfinder. (A logic of evidence evaluation would try to capture the acceptable patterns of reasoning as plausibility schemas.) The choice of pattern depends upon the nature of the issue of fact to be proved and the nature of the available evidence. When patterns of evidence are linked or attached to the terminal propositions of the inverted rule tree, they extend the branches of that tree further downward. As the schematic in Figure 2 suggests, the complete logical model for the legal reasoning in a particular case (the “inference tree” for the case) has the shape of an inverted triangle, with the implication tree generating the upper branches of the triangle and the attached patterns of evidence evaluation extending those branches downward to the evidentiary assertions.

After the factfinder organizes the evidence by relevance, evaluation can proceed upward from the bottom of the extended tree. After the factfinder assigns plausibility-values to the evidentiary assertions, the instantiated plausibility schemas warrant the plausibility-values of higher-level assertions. At the point in each branch where the evidentiary assertions end and the condition of a rule occurs, the applicable standard of proof directs the factfinder about how to make a finding of fact based on the plausibility of the evidence. A preponderance-of-evidence standard is the rule that a factfinder must find the issue of fact to be “true” if the totality of relevant evidence is to any degree plausible, and must find the issue of fact to be “false” if that evidence is to any degree implausible. In addition, the legal rules on burden of persuasion determine which party must lose (which finding to make) if the evidence is “undecided” or in equipoise. Discovering the logic of legal reasoning means making this process of evidence evaluation transparent.

Devising a useful, normative logic of factfinding is even more difficult because of the pragmatic and dynamic nature of the factfinding process. Factfinders must make findings in real time, using limited resources, and on the basis of the incomplete evidence. Moreover, the factfinding process is often highly structured around the factfinder, with participants other than the factfinder deciding what the legal rules are and producing evidence on the record. As a result, all conclusions are usually only tentative and subject to revision. New evidence, or a reanalysis of old evidence, can defeat an earlier conclusion or undermine its evidentiary support. A change in rules may modify what lines of reasoning are acceptable. Yet at each stage of the legal proceeding, it must be reasonable to rely upon each provisional conclusion. These four characteristics of evidence evaluation — that it is practical, dynamic, defeasible, and presumptively sound — make it an exemplary instance of what logicians call “default reasoning.” Default reasoning uses the available evidence, together with default inference rules, to warrant presumptive conclusions, which are then subject to future revision. The highly structured framework in which law accomplishes evidence evaluation poses significant challenges to traditional logic.

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