We then turn to a recent u-turn on his part, in which he winds up rescinding his commitment toModus Ponens, on the grounds of a tension with the rule of Import-Export for conditionals. Here we offer an important positive contribution to the literature, settling the following crucial question that Bradley leaves unanswered: Assuming that one gives up on full-blown Modus Ponens on the grounds of ...

T-norm based fuzzy logics are usually considered as truth preserving, that is, taking 1 as the only truth value to be preserved in inferences. In this paper we study t-norm based fuzzy logics preserving degrees of truth, that is, preserving the lower bounds of the truth degrees of the premises. These logics are axiomatizable by using a restricted form of Modus Ponens together with the rule of A...

Conditional deduction in binary logic basically consists of deriving new statements from an existing set of statements and conditional rules. Modus Ponens, which is the classical example of a conditional deduction rule, expresses a conditional relationship between an antecedent and a consequent. A generalisation of Modus Ponens to probabilities in the form of probabilistic conditional inference...

In order to analyze the logical foundation of fuzzy reasoning, this paper first introduces the concept of generalized roots of theories in Łukasiewicz propositional fuzzy logic Łuk, Gödel propositional fuzzy logic Göd, Product propositional fuzzy logic P, and nilpotent minimum logic NM (the R0-propositional fuzzy logic L ). Next, it is proved that all consequences of a theory C, named D(C), are...

We will begin by defining some logical connectives. The first logical connective is implication. Luckily, implication is already built in to the Haskell type system in the form of arrow types. The type p -> q is equivalent to the logical statement P → Q. We can now prove a very simple theorem called Modus Ponens. Modus Ponens states that if P implies Q and P is true, then Q is true. It is often...

This article presents and discusses a prima facie counterexample to modus ponens. To appropriately theorize the case, I argue for conceptualizing notions of logical consequence commitment in “normative” terms, so that does not attach premises spurious dominance argument—and, more generally, unreasonable decision states, or syntactically specified classes thereof. also suggest there is motivatio...

There are two primary arguments against scientific realism, one pertaining to underdetermination, the other to the history of science. While these arguments are usually treated as altogether distinct, P. Kyle Stanford’s ‘problem of unconceived alternatives’ constitutes one kind of synthesis: I propose that Stanford’s argument is best understood as a broad modus ponens underdetermination argumen...

Knowledge representation of reasoning processes is a central notion in the field of artificial intelligence, especially for knowledge-based agents, because such representation facilitates knowledge of action outcomes necessary for optimum performance by problem-solving agents in complex situations. Logic is the primary vehicle by which knowledge is represented in knowledge-based agents. It invo...