Related papers: Implicational Completeness
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae { A \_i | i$\ge$1} by letting A\_1 be A and A\_{i+1} be A(A\_i/x). Ruitenburg's Theorem [8] says…
We prove that the sequent calculus $\mathsf{L_{RBL}}$ for residuated basic logic $\mathsf{RBL}$ has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic $\mathsf{BPL}$. Thus…
In this paper, we extend the sequent calculus LKF into a calculus LK(T), allowing calls to a decision procedure. We prove cut-elimination of LK(T).
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
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…
Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determ- ining provability of bounded depth formulas in the…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary…
We introduce the notion of being Weihrauch-complete for layerwise computability and provide several natural examples related to complex oscillations, the law of the iterated logarithm and Birkhoff's theorem. We also consider hitting time…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
We prove a topological completeness theorem for the modal logic GLP containing operators $\langle\lambda\rangle$ for $\lambda \in$ Ord intended to capture progressively stronger notions of consistency in mathematical theories. We show that,…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
This paper describes how automated deduction methods for natural language processing can be applied more efficiently by encoding context in a more elaborate way. Our work is based on formal approaches to context, and we provide a tableau…
We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.