Related papers: Formal Theories for Logspace Counting
We introduce two-sorted theories in the style of [CN10] for the complexity classes \oplusL and DET, whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys' linear algebra theory…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…
This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I,…
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
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…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…
This papers is concerned with multisymplectic formalisms which are the frameworks for Hamiltonian theories for fields theory. Our main purpose is to study the observable $(n-1)$-forms which allows one to construct observable functionals on…