Related papers: Tarski's relevance logic; Version 2
The Alexandrov topology affords a well-known semantics of modal necessity and possibility. This paper develops an Alexandrov topological semantics of intuitionistic propositional modal logic internally in any elementary topos. This is done…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
Lindstr\"om theorems characterize logics in terms of model-theoretic conditions such as Compactness and the L\"owenheim-Skolem property. Most existing characterizations of this kind concern extensions of first-order logic. But on the other…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…
We prove the following version of the first incompleteness theorem that simultaneously strengthens Mostowski's theorem and Vaught's theorem: For any c.e. family $\{ T_i \}_{i \in \omega}$ of consistent extensions of Tarski, Mostowski and…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
Team Semantics generalizes Tarski's Semantics for First Order Logic by allowing formulas to be satisfied or not satisfied by sets of assignments rather than by single assignments. Because of this, in Team Semantics it is possible to extend…
Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such…
We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailment of formulas. We prove the logic is complete in Pavelka…
We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question whether they are generated by a finite set of operations. We obtain…
Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…
This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifies the usual notion of logical consequence by stipulating…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…
In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can…
Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two…