Related papers: Composition of inverse problems with a given logic…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…
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…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a…
Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…
We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional…