New Foundations for Imperative Logic I: Logical Connectives, Consistency, and Quantifiers*

Abstract

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied-what more is there to say? Much more, I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three-valued imperatives which mixes declaratives with imperatives. I develop such a logic.

A Formalism for Action Representation Inspired by Mīmāṁsā

“…To address the dilemma raised by Jørgensen, Peter Vranas proposed three values for imperatives, namely Satisfaction (S ), Violation (V ) and Avoidance (A), in the work of constructing a logic for imperatives [18]. An imperative holds one of the three values, either S , V or A.…”

“…Much of the work in logical reasoning is concentrated on declarative sentences [10,18]. However, some logicians and philosophers have noticed the logical properties of imperatives [4,5,11].…”

“…But in doing so, they suffer from Jørgensen's dilemma [5], where on one hand, inference follows the premises, while on the other hand, since imperatives do not hold the value of true or false, these fall outside the realm of classical logic. To overcome this difficulty, Peter Vranas suggested a formalism that treats imperatives as a basic unit [18]. Continuing with this notion, this paper presents a goal oriented approach in the treatment of imperatives while considering the underpinnings of artificial intelligence.…”

“…To this end, enormous amount of research is being done in the area of knowledge representation and reasoning, wherein formalism for representation is constructed and utilized for the logical reasoning process. This process is based on the approach that involves propositions [18]. But in the realm of interaction with computers, instructions 1 play a vital role.…”

The property of rationality: a guide to what rationality requires?

“…Avoidance has been commonly assumed to hold true for requirements that are represented by a code satisfying (NC) (see, for example, Broome 2007b, p. 38;2013a;Lord 2011;Hill 1973;Schroeder 2004Schroeder , 2005and Vranas 2008).…”