Related papers: The Discrete-Continuous Logic and its possible qua…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
In arXiv: math.LO/0011208 we proposed the {\sl intuitionistic or disjunctive representation of quantum logic}, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
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…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
Propositional Dynamic Logic, PDL, is a modal logic designed to formalize the reasoning about programs. By extending accessibility between states to states and state sets, concurrent propositional dynamic logic CPDL, is introduced to include…
Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…
Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more…
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…
Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…