# Questions tagged [lo.logic]

Computational and mathematical logic.

518 questions
Filter by
Sorted by
Tagged with
1 vote
67 views

### To what extent supervised learning ERM learn first-order knowledge

Suppose I have a collection of (hidden) first-order rules: $$\mathcal{R}: \{ Q_i(x) => P_i(x) \}_{i=1}^{k}$$ all defined over $x \in \mathcal{X}$. I can use these rules and (automatically) ...
• 749
117 views

• 22.4k
264 views

### Is Agda sound as a proof system? [closed]

I've asked the same question on CSSE but with no luck (https://cs.stackexchange.com/questions/89611/is-agda-sound-as-a-proof-system). Therefore I ask it again here in cstheory and hope that more ...
• 251
1k views

### Sparsification Lemma for k-SAT and Exponential Time Hypothesis

According to R. Impagliazzo, R. Paturi and F. Zane, 2001 an instance of $k$-SAT is called sparse if $m = O(n)$ where $m$ denotes the number of clauses and $n$ the number of variables. The ...
• 1,977
154 views

### Is Eulerian Path (or Eulerian Cycle) definable in Monadic Second Order Logic?

Does there exist a monadic second order logic formula which is satisfied by a graph if and only if it has an Eulerian path (or Eulerian cycle). I am looking for properties of graphs which are ...
279 views

### Fischer and Rabin's theorem (1974) for theories of "additive" structures

Fischer and Rabin's Super-Exponential Complexity of Presburger Arithmetic (1974) has the following theorem. (Theorem 12) Let $U$ be any class of additive structures, so if $A = (A, +) \in U$, ...
• 885
56 views

### Is there a complete and finite axiom scheme for conditional independence? (Graphoids)

Note: This is a better-written version of an unanswered question asked before on MathOverflow. Question: Is there a complete and finite axiom scheme for conditional probability? If so, is there a ...
• 503
159 views

### Connection between algebraic logic and computational complexity of logics?

I'm learning a bit about algebraic logic and I was wondering how knowing the algebraic semantics of a given logic might help the study of the logic itself from a computational point of view. In ...
• 1,406
484 views

### Complexity of modal logic IK5

What is the complexity of local satisfiability problem for modal logic $\mathit{IK5}$? Herein we denote by $IK5$ the modal logic over euclidean frames extended with inverse modality. Could you provide ...
• 1,165
367 views

### Philosophy behind monotonicity requirement for inductive types

Is there a good philosophical reason for why inductive types with negative occurrences or non-monotonicity should not be considered valid constructions? According to my understanding of the Bishop/...
• 247
53 views

• 22.4k
129 views

### Family of formulas for which Gabbay's separation algorithm explodes nonelementarily

It is repeated throughout the literature that Gabbay's algorithm for separation of LTL with Since and Until can produce nonelementary blow-up of the size of the formula, but I have never seen a proof ...
284 views

### Normal forms for intuitionistic formulas?

It is well-known that DNFs/CNFs and prenex normal forms generally do not exist for intuitionistic logic. Are there any nice results about formula normalization for IL? I've tried googling this but ...
• 247
1 vote
86 views

• 712
1 vote
180 views

• 1,977
141 views

### Salomaa's axiomatisation of regular languages and the use of regular expression in it

I am reading the classical article of A. Salomaa where he gives two axiom systems for regular sets and proofs consistency and completeness. As I have understood it, an axiomatic system in some logic (...
• 1,977
159 views

### How to mechanically derive the recursor of a type from its constructors?

In Martin-Löf Dependent Type Theory a type is commonly prescribed by how to construct its canonical terms and how to show that its canonical terms are definitionally equal. This means that the ...
• 777
933 views

### Does the uncomputability of Kolmogorov complexity follow from Lawvere's Fixed Point Theorem?

Many theorems and "paradoxes" - Cantor's diagonalization, undecidability of hatling, undeciability of Kolmogorov complexity, Gödel Incompleteness, Chaitin Incompleteness, Russell's paradox, etc. -...
• 36.3k
875 views

• 32.1k