A finitely Axiomatizable complete theory with atomless F1 (T).
A first order probability logic – .
A First-Order Conditional Probability Logic With Iterations
A first-order logic for multi-algebras.
A formal analysis of musical scores
A formalization of the Lewis system S1 without rules of substitution.
In the Lewis and Langford formalization of system S1 (1932), besides the deduction rules, the substitution rules are as well used: the uniform substitution and the substitution of strict equivalents. They then obtain systems S2, S3, S4 and S5 adding to the axioms of S1 a new axiom, respectively, without changing the deduction rules. Lemmon (1957) gives a new formalization of systems S1-S5, calling them P1-P5. Is is worthwhile to remark that in the formalization of P2-P5 one does not use any more...
A fuzzy and intuitionistic fuzzy account of the Liar paradox.
The Liar paradox, or the sentenceI am now saying is falseits various guises have been attracting the attention of logicians and linguists since ancient times. A commonly accepted treatment of the Liar paradox [7,8] is by means of Situation semantics, a powerful approach to natural language analysis. It is based on the machinery of non-well-founded sets developed in [1]. In this paper we show how to generalize these results including elements of fuzzy and intuitionistic fuzzy logic [3,4]. Basing...
A general deduction theorem.
In this paper we present a very general deduction theorem which -based upon a uniform notion of proof from hypotheses- holds for a very large class of logical systems. Most of the known results for classical and modal logics, as well as new results, are immediate corollaries of this theorem.
A generalization of a formalized theory of fields of sets on non-classical logics [Book]
A generalization of the propositional calculus for purposes of the theory of logical nets with probabilistic elements
A graphical representation of relational formulae with complementation
We study translations of dyadic first-order sentences into equalities between relational expressions. The proposed translation techniques (which work also in the converse direction) exploit a graphical representation of formulae in a hybrid of the two formalisms. A major enhancement relative to previous work is that we can cope with the relational complement construct and with the negation connective. Complementation is handled by adopting a Smullyan-like uniform notation to classify and decompose...
A graphical representation of relational formulae with complementation∗
We study translations of dyadic first-order sentences into equalities between relational expressions. The proposed translation techniques (which work also in the converse direction) exploit a graphical representation of formulae in a hybrid of the two formalisms. A major enhancement relative to previous work is that we can cope with the relational complement construct and with the negation connective. Complementation is handled by adopting a Smullyan-like...
A Hierarchy of Automatic ω-Words having a Decidable MSO Theory
We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSO-interpretability in algebraic trees, and the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is in a certain sense canonical. We then generalize our techniques to a hierarchy of classes of ω-words enjoying the above...
A Kalmár-style completeness proof for the logics of the hierarchy
The logics of the family := are formally defined by means of finite matrices, as a simultaneous generalization of the weakly-intuitionistic logic and of the paraconsistent logic . It is proved that this family can be naturally ordered, and it is shown a sound and complete axiomatics for each logic of the form . The involved completeness proof showed here is obtained by means of a generalization of the well-known Kalmár’s method, usually applied for many-valued logics.
A Logic for Reasoning About Qualitative Probability
A Logic of Approximate Reasoning
A Logic with Big-stepped Probabilities That Can Model Nonmonotonic Reasoning of System P
A Logic with Conditional Probability Operators
A Logic With Higher Order Conditional Probabilities
A Logic With Higher Order Probabilities