Logicians treat assertions as true, believed or merely hypothesized sentences. The reasoner who uses them, however, is the sole referee who can validate their truth, their aptness to describe an actual situation, their strength (as beliefs) or the relevance of their use in the current logical context. Moreover, the reasoner actively counts on these factors, as part of the reasoning process itself, and should normally be capable, when asked to do so, to assign consistently relative strengths to the assertions used. The paper assumes, first, that assertions have -each- an associated, measurable strength, and that, second, this strength has significant -and measurable- effects on the truth of the sentences, the validity of the conclusion and the soundness of the reasoning. The concepts and formulas required for this are explored, and a semantics and proof theory for a sentential calculus of assertions are proposed as a natural extension of ordinary two-valued reasoning. The resulting theory, though reminiscent of Probability,is autonomous, self-contained and of a purely logical nature.

A new problem about 'if...then...' is posed which is related to Curry's paradox much as the barber's paradox parallels Russell's paradox. However, it is not obvious how to solve it.

Beyond any doubt the pragmatical-based improvements introduced in the rules of inference during the process of refinement of a legal expert system may be efficient but they hardly will be capable to provide a point of reference for a more general correctness measure. During the refinement of KBSLEX the debate of the Theory of Legal Argument has contributed to illuminate the point suggesting that the modeling of legal reasoning and legal decision making should be grounded on a logical approach but without limiting itself to the tools of the classical logic.

Classical approaches such as frames, scripts,... have been unable to deal with the kind of inferences necessary in natural language processing situations such as text comprehension. Shastri & Ajjanagadde (1993), proposed a local connectionist model for the sort of reasoning requiring such a fast inference. The problem with this system is that it controls only the adequacy of argument- fillers, leaving untouched the activation control issue, namely, why we perform certain inferences, and not others, in a given situation. The aim of this paper is to examine how a focus, in the sense of Grosz (1981). could operate as a theoretic constraint with the above reasoner system to handle two aspects: inference control and anaphora resolution (i.e., antecedent activation), during text understanding.

Attempts to give a Logic or Semantics for vague predicates and to defuse the Sorites paradoxes have been largely a failure. We point out yet another problem with these predicates which has not been remarked on before,namely that different people do and must use these predicates in individually different ways. Thus even if there were a semantics for vague predicates, people would not be able to share it. To explain the occurrence nonetheless of these troublesome predicates in language, we propose a different approach based on asking the question, “How do these vague predicates help people to communicate with each other?” We show that in general, even though different people assign different extensions to vague predicates, they usually benefit from receiving information framed in terms of them.

The aim of this paper is to investigate the preconditions and the limits of rational reconstruction in the philosophy of language, as these preconditions and limits can be deduced from Wittgenstein’s arguments against philosophical constructivism. It will be shown that a main precondition of reconstructions in the field of language is the existence of non-arbitrary patterns of linguistic use, while the limits of this kind of theoretical enterprise derive precisely from the absence of such patterns.

The main purpose of this paper is to show that Kant’s transcendental philosophy is tacitly laden with the structures of modern modal thought. More exactly, the surprising parallelism which seems to exist between Kant’s manner of defining necessity (and, on this basis, nomicity) and the modern approaches of the same concepts in the frame of “possible worlds philosophy” is stressed. A new interpretation of the Categorical Imperative is also offered on this basis.

This short paper about fuzzy set-based approximate reasoning first emphasizes the three main semantics for fuzzy sets: similarity, preference and uncertainty. The difference between truth-functional many-valued logics of vague or gradual propositions and non fully compositional calculi such as possibilistic logic (which handles uncertainty) or similarity logics is stressed. Then, potentials of fuzzy set-based reasoning methods are briefly outlined for various kinds of approximate reasoning: deductive reasoning about flexible constraints, reasoning under uncertainty and inconsistency, hypothetical reasoning, exception-tolerant plausible reasoning using generic knowledge, interpolative reasoning, and abductive reasoning (under uncertainty). Open problems are listed in the conclusion.

This paper deals with the relation with Fuzzy Logic of some of the ideas of Karl Menger published between 1942 and 1966 and concerning what he called “Hazy Sets”, Probabilistic Relations and Statistical Metric Spaces. The author maintains the opinion that if Lofti A. Zadeh is actually the father of Fuzzy Logic, Menger not only was a forerunner of this field but that his ideas were and still are influential on it.

The paper proposes a typology of the scientific theories based on the modality of mathematizing (relying on the kind of mathematics which participates to the theory edification and the level of mathematical organizing of the theoretical frame). This gives us, like the classification of the geometries from the famous -Erlagen Program- initiated by Felix Klein, an internal principle for the connection of the different forms or levels of the theorizing, a constructive basis for the understanding of the complex structural nets of the mature scientific disciplines.

The aim of my paper is to explore in some detail some epistemological issues concerning moral theorizing on global warming. First, I consider the issue of the structure of the theoretical approach in a field of inquiry requiring normative assessments. How do theoretical principles work here? What is to be regarded as a normative evidence for such a theory? Second, the criteria to determine which part, if any, of the theory gets normatively constrained, and which does not, are discussed. Third, I focus on the procedures to reach an equilibrium between such a theory and its evidence and to reach it, changes might be required on the normative side of the theory, rather than on its non-normative one

This paper presents aprevalent representation about the objectivity and impartiality of scientific knowledge that emerges from the structure and style of the standard research paper. This representation is critically examined considering some rather untypical scientific papers reporting controversies between researchers in a certain field of experimental science. The role of personal preconceptions and intellectual prejudices in the assessment of scientific theories is emphasized by reference to Einsteinls grounds for his general theory of relativity.

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence.

Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional logic -results traditionally credited to Bernays (1918) and Post (1921). These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its soundness and completeness: a sentence is provable if and only if valid. By 1917, strongly influenced by PM, Hilbert accepted the theory of types and logicism -a surprising shift. But by 1922 he abandoned the axiom of reducibility and then drew back from logicism, returning to his 1905 approach of trying to prove the consistency of number theory syntactically.