Related papers: Propositional Measure Logic
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They…
We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…