Algorithmic Decision of Syllogisms

Cognitive Science, 2017

A recent meta-analysis (Khemlani & Johnson-Laird, 2012) about psychological experiments of syllogistic reasoning demonstrates that the conclusions drawn by human reasoners strongly deviate from conclusions of classical logic. Moreover, none of the current cognitive theories predictions fit reliably the empirical data. In this paper, we show how human syllogistic reasoning can be modeled under a new cognitive theory, the Weak Completion Semantics. Our analysis based on computational logics identifies seven principles necessary to draw the inferences. Hence, this work contributes to a computational foundation of cognitive reasoning processes.

2021

The presented empirical research is based on a new model for the categorical syllogisms, described and partially tested elsewhere. This model assumes that deriving a conclusion involves a pattern completion process, similar to the completion of perceptual patterns. Specifically, inferring a conclusion would require the generation of the missing part of an abstract pattern of logical semantic features. This pattern is named schema, because it is organized around a particular argumentative goal. Such a schema emerges through the frequent contact with a corresponding class of argumentative experiences. As, presumably, the usual pragmatic argumentative contexts imply predominantly valid syllogisms, pragmatic syllogistic schemas would emerge mainly for them. These pragmatic schemas for the valid syllogisms are supposed to be based on a particular mixed semantics of their syllogistic judgments, including both intensional (class-property) and extensional (subclass-class) relationships. The...

2008

In traditional propositional logic, many replacement and inference rules were involved to ascertain if the truth of several antecedents implied the truth of a particular consequent. This research described a powerful technique called the Modern Syllogistic Method (MSM), which ferreted out from a set of premises all that can be concluded from it and casted the resulting conclusions in the simplest and most compact form. We observed that all replacement rules were explicitly and inherently integrated within the MSM and proved that all inference rules were simply limited special cases of it. This meant that the MSM constituted a complete method of logic deduction. We also showed how to use the MSM in determining whether inconsistencies existed within a given set of premises and also in detecting formal logical fallacies. We demonstrated the applicability of the method in diverse fields via four examples that illustrated its mathematical details and exhibited the nature of conclusions it can come up with. In fact, these examples demonstrated the possibility of extracting deductions that were not so obvious and even surprising. The examples also showed how logic can be misused and how logic misuse can be avoided or detected.

In traditional propositional logic, many replacement and inference rules are involved to ascertain if the truth of several antecedents implies the truth of a particular consequent. This paper describes a more powerful technique called the modern syllogistic method. This method is shown to ferret out from a set of premises all that can be concluded from it, with the resulting conclusions cast in the simplest compact form. We observe that all replacement rules are explicitly and inherently integrated within the modern syllogistic method, and prove that all inference rules are simply limited special cases of it. This means that the modern syllogistic method constitutes a complete method of logic deduction. We also show how to use the modern syllogistic method in determining whether inconsistencies exist within a given set of premises and also in detecting formal logical fallacies. We demonstrate the applicability of the method in many diverse fields via a large number of examples that illustrate its mathematical details and exhibit the nature of conclusions it can come up with. In fact, these examples demonstrate the possibility of extracting deductions that are not so obvious and even surprising. The examples also show how logic can be misused, and how logic misuse can be avoided or detected.

Topics in Cognitive Science, 2020

Syllogistic reasoning, that is the drawing of inferences for categorical-quantified assertions, is one of the oldest branches of deductive reasoning research with a history exceeding 100 years. In syllogistic reasoning experiments, "No Valid Conclusion" (NVC) is one of the most frequently selected responses and corresponds to the logically correct conclusion for 58% of the syllogistic problem domain. To date, NVC is often neglected in computational models or just treated as a by-product of the underlying inferential mechanisms such as a last resort when the search for alternatives is exhausted. We illustrate that NVC represents a major shortcoming of current models for human syllogistic reasoning. By introducing heuristic rules for predicting NVC, we demonstrate that simple extensions of the existing models result in substantial improvements in their predictive performances. Our results emphasize the need for better NVC handling in cognitive modeling of human reasoning and provide directions for modelers on how to enhance their approaches.