Related papers: Arithmetics within the Linear Time Hierarchy

Motivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras (Reshetikhin and Turaev), monoidal categories…

We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…

Symmetry under time-reversal appears in the microscopic description of many physical systems. In a quantum mechanical setting it acts as an anti-unitary operator, so does not fall under general analyses based on unitary symmetries. In…

Pointer arithmetic is widely used in low-level programs, e.g. memory allocators. The specification of such programs usually requires using pointer arithmetic inside inductive definitions to define the common data structures, e.g. heap lists…

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…

We investigate the expressive power of quantifier alternation hierarchy of first-order logic over words. This hierarchy includes the classes ${\Sigma}_i$ (sentences having at most $i$ blocks of quantifiers starting with an $\exists$) and…

We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k…

Let $\RR_S$ denote the expansion of the real ordered field by a family of real-valued functions $S$, where each function in $S$ is defined on a compact box and is a member of some quasianalytic class which is closed under the operations of…

Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…

It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…

"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…

This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…

We study when a sound arithmetic theory $\mathcal S{\supseteq}S^1_2$ with polynomial-time decidable axioms efficiently proves the bounded consistency statements $Con_{\mathcal S{+}\phi}(n)$ for a true sentence $\phi$. Equivalently, we ask…

Terms in arithmetic of the form s in the formula s=t(< s >), with t a term with one free variable and < s > a numeral denoting the G\"odel number of s, are examined by writing the explicit definition of the encoding functions whose…

We streamline treatments of the interpretability orders $\trianglelefteq^*_\kappa$ of Shelah, the key new notion being that of pseudosaturation. Extending work of Malliaris and Shelah, we classify the interpretability orders on the stable…

Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…

In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…

In a recent paper by Chen et al. [8], the authors initiated the control-theoretic study of a class of discrete-time multilinear time-invariant (MLTI) control systems, where system states, inputs, and outputs are all tensors endowed with the…

The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…

Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…