Two experiments examine speed-up in argument pairs of various propositional forms. In the first experiment, participants were presented with pairs of conditional arguments. Some of these pairs had a form of a valid Modus Ponens (MP) inference, whereas other pairs had a form of a fallacy of Affirming the Consequent (AC). In both argument pairs, presentation of the prime led to a significant spee...

Ex. 17 Let us call the new system L, i.e. its axioms are all propositional tautologies (Axiom 1) plus the axioms 2> (Axiom 2) and 2φ∧2ψ → 2(φ∧ψ) (Axiom 3), and the rules modus ponens and φ→ ψ 2φ→ 2ψ We have to show that for all formulas φ `K φ ⇔ `L φ. ⇒: For this direction we have to show that L derives all axioms of K and all its rules. Axiom 1 of K is the same as Axiom 1 in L, thus we have no...

Two competing theories of processing of conditionals (if-then) were tested. Syntactic theories posit that people only draw inferences conforming to the logically valid modus ponens (MP) schema. Mental models theories predict that people draw MP and invalid affirming-the-consequent (AC) inferences. Three experiments tested these predictions. Participants read short stories that conformed to eith...

Lorenzen dialogues provide a two-player game formalism that can characterize a variety of logics: each set S of rules for such a game determines a set D(S) of formulas for which one of the players (the socalled Proponent) has a winning strategy, and the set D(S) can coincide with various logics, such as intuitionistic, classical, modal, connexive, and relevance logics. But the standard sets of ...

The most obvious bimodal logic generated from unimodal logics L1 and L2 is their fusion, L1 ⊗L2, axiomatized by the theorems of L1 for 1 and of L2 for 2, and by the rules of modus ponens, substitution and necessitation for 1 and for 2. Shehtman introduced the frame product L1×L2, as the logic of the products of certain Kripke frames. Typically, L1 ⊗ L2 ( L1 × L2, e.g. S4⊗ S4 ( S4× S4. Van Benth...

Rule based reasoning (RBR) and case based reasoning (CBR) have emerged as two important and complementary reasoning methodologies in artificial intelligence (AI). For problem solving in complex, real world situations, it is useful to integrate RBR and CBR. This paper presents an approach to achieve a compact and seamless integration of RBR and CBR within the base architecture of rules. The pape...

We present in this paper a formal theory of reasoning by analogy. We are mainly concerned with three subjects : a formal definition of analogy, a formalization of the reasoning in terms of deduction, and a method for realizing the reasoning in a logic programming system. First we assume that each domain for the reasoning is the least model for logic program. Then we consider an analogy as a par...

We devote this paper to the completeness of an axiom system for PDL0 — a variant of PDL which includes the program operations of composition and intersection. Most of the difficulty in the proof of the completeness theorem for PDL0 lies in the fact that intersection of accessibility relations is not modally definable. We overcome this difficulty by considering the concepts of theory and large p...

This paper begins with a review of the literature on plausible reasoning with deductive arguments containing a conditional premise. There is concurring evidence that people presented with valid conditional arguments such as Modus Ponens and Modus Tollens generally do not endorse the conclusion, but rather find it uncertain, in case (1) the plausibility of the major conditional premise is debata...

The logic of single-conclusion (functional) proofs (FLP) is introduced. It combines the veri$cation property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that FLP is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicate...